
Book 



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WORKS OF 
GEORGE CHANDLER WHIPPLE 

PUBLISHED BY 

JOHN WILEY & SONS, INC. 



The Microscopy of Drinking Water. 

Third Edition, Rewritten and Enlarged. 

With a Chapter on the Use of the Microscope, by John 

W. M. Bunker, Ph.D. 

xxi + 409 pages. 6 by 9. 74 figures, 6 full-page plates 

in the text, and 19 plates of organisms in colors. Cloth, 

$4.00 net. 

Vital Statistics. " 

xii + 517 pages. 4| by 7. 63 figures. Flexible " Fab- 
rikoid" binding, $4.00 net. 



By henry BALDWIN WARD 

AND 

GEORGE CHANDLER WHIPPLE 

AND ASSOCIATES 

Fresh- Water Biology. 

ix + 1111 pages. 6 by 9. 1547 figures. Cloth, $6.00 
net. 



VITAL STATISTICS 

AN INTRODUCTION TO THE SCIENCE 
OF DEMOGRAPHY 



BY 

GEORGE CHANDLER WHIPPLE 

Professor of Sanitary Engineering in Harvard University 

Member of the Public Health Council, Massachusetts 

State Department of Health 



FIRST EDITION 



NEW YORK 

JOHN WILEY & SONS, Inc. 

London: CHAPMAN & HALL, Limited 
1919 







% 



Copyright, 1919, 

BY 

GEORGE CHANDLER WHIPPLE 



MAf -9 i9iy 



\l 



Stanbopc iprcss 

F. H. GILSON COMPANY 
BOSTON, U.S.A. 

©CU5^54i3 



DEDICATED TO 

THE STUDENTS OF VITAL STATISTICS 

IN THE SCHOOL OF PUBLIC HEALTH 

OF HARVARD UNIVERSITY 

AND THE 

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 



PREFACE 

This book is written for students who are preparing them- 
selves to be pubhc health officials and for public health 
officials who are willing to be students. It makes no claim 
to be an exhaustive treatise or a compendium of facts; 
it is merely a guide to the study of vital statistics, an 
introduction to the great- world-wide science of demogra- 
phy — a science yet in the magmatic stage, not yet crystal- 
lized. The Great War is bound to develop this science, 
because hereafter all the nations of the earth must know each 
other better, and this knowledge, in order to be usable, must 
be condensed into statistical forms. 

Specifically the book tells what statistics are and what 
they are not; it shows how to express vital facts by figures, 
how to tabulate them and how to display them by diagrams; 
it shows how to compute birth-rates and death-rates and 
how to analyze a death-rate; it shows how to adjust and 
standardize death-rates and how to make life tables; it em- 
phasizes the need of using vital statistics with truth, with 
imagination and with power. 

For the convenience of school instruction, exercises and 
questions to incite further study are given in each chapter. 
Many subjects worthy of special study, however, are not 
even mentioned, loose ends have been left in every chapter, 
illustrations have been chosen as they came conveniently to 
hand, and the general arrangement has beeninformal as to its 
subject matter. The object in all this has been to stimulate 
the reader to critically analyze all vital statistics as they ap- 
pear before him from day to day. Although the illustrations 
have been gathered in a haphazard way, an attempt has been 
made to set forth the elementary principles of the statistical 
method in a simple and orderly fashion. 

V 



vi PREFACE 

The author wishes to confess that he is not an authority 
on vital statistics, much less an authority on demography; 
he is merely a student of the science. He has taken the 
student's privilege of quoting freely from many writers to 
whom he wishes to render acknowledgments and thanks. 
In particular he desires to express his obligations and personal 
regards to Dr. William H. Davis, Chief Statistician for Vital 
Statistics, United States Bureau of the Census, who has read 
the entire proof of this book and given the benefit of his 
careful criticism. 

Just a personal word to the health officers of America. 
A new day is dawning for you. The care of the public 
health is becoming a distinct profession. The medical pro- 
fession alone is not able to cope with it. The young men 
and women who are to be the executive health officers in the 
next generation are recognizing the need of special training, 
based on the principles of preventive medicine, hygiene and 
sanitation. Schools of public health are coming into exist- 
ence and receiving warm-hearted support. The health ad- 
ministration of the future will be. in the hands of full-time 
officials, who are adequately paid and protected in their 
tenure of office, but who in return for these advantages must 
be adequately trained for their work. The ability to use 
vital statistics in public health work is an important part 
of this training. Many of you have been in office for a long 
time, you have forgotten most of your arithmetic — not to 
mention algebra. You can see the new era coming and you 
dread the new' methods founded on accurate statistical studies 
of accident, disease and death. There is no need of this fear. 
You can use statistics as well as any one, but you must study. 
This book has been prepared with your difficulties in mind. 

GEORGE CHANDLER WHIPPLE 

Cambridge, Mass. 
January, 1919. 



Page 



CONTENTS 

CHAPTER I 

DEMOGRAPHY 

Principal divisions of demography — Demography both old and 
new — History of statistics — Celebrated demographers — Sec- 
tion of Vital Statistics — The statistical method — Need of the 
statistical method — Why statistics are thought to be dry — Can 
you prove anything by statistics? — National bookkeeping — Sta- 
tistics necessary for health officer — National vital statistics — 
Statistical induction — Choice of statistical data 1 

CHAPTER II 

STATISTICAL ARITHMETIC 

Statistical processes — Collection of data — Statistical units — 
Errors of collection — Tally sheets — Tabulation — Inexact 
numbers — Precision and accuracy — Combinations of inexact 
numbers — Ratios — Rates — Misuse of rates — Index — Com- 
putation of rates — Logarithms — The slide-rule — Classification 
and generalization — Classes, groups, series and arrays — Gen- 
eralizations of classes and groups — The array and its analysis — ' 
Groups — Group designations — Percentage grouping — Cumu- 
lative grouping — Averages — The moving average — Mechanical 
devices 17 

CHAPTER III 

STATISTICAL GRAPHICS 

Use of graphic methods — Types of diagrams — The appeal to 
the eye — Graphical deceptions — Essential features of a diagram 

— One-scale diagrams — Diagrams with rectangular coordinates 

— Use of the horizontal scale — Plotting figures by groups — 

vii 



VIU CONTENTS 

Page 
Plotting irregular groups — Summation diagrams — Choice of 

scales — Diagrams with polar coordinates — Double coordinate 
paper — Ratio cross-section paper — Logarithmic cross-section 
paper — Ruled paper — Mechanics of diagram making — Letter- 
ing — Wall charts — Use of color in diagrams — Component part 
diagrams — Statistical maps — Blue prints and other prints — 
Reproduction of diagrams — Equation of curves 58 

CHAPTER IV 

ENUMERATION AND REGISTRATION 

United States census — The census date — Civil divisions — 
Enumeration schedule of 1910 — Bowley's rules for enumeration 

— Credibility of census returns — State censuses ' — Registration 
and notification — Registration of births — Advantages of birth 
registration — Evidences of incomplete registration — Enforce- 
ment of registration law — Registration of deaths — Uses of 
death registration — Marriage registration — Morbidity regis- 
tration — Notifiable diseases — Incompleteness of morbidity 
statistics — Morbidity from non-reportable diseases — Reporting 
venereal diseases — Sickness surveys — Other methods of securing 
data — United States registration area for deaths — United States 
registration area for births — Need of national statistics 100 

CHAPTER V 

POPULATION 

Estimation of population — Arithmetical increase — Adjust- 
ment of population to mid-year — Geometrical increase — For- 
mula for geometrical increase — Rate of increase — Decreasing 
rate of growth — Difference between estimate and fact. Revised 
estimates — Estimation of population from accessions and losses 

— Estimation of future population — Immigration — Graphi- 
cal method of estimating population — Accuracy of state cen- 
suses — Urban and rural population — Density of population — 
Population of United States cities — Metropohtan districts — 
Classification of population — Color, race, nativity, parentage — 
Sex distribution — Dwellings and families — Age distribution — 
Census meaning of age — Errors in ages of children — Errors 



CONTENTS IX 

Page 
due to use of round numbers — Other sources of error — Age- 
groups — Persons of unknown age — Redistribution of population 
— Redistribution for non-censal years — Progressive character of 
age distribution — Types of age distribution — Standards of age 
distribution — Age distribution of people of United States 129 



CHAPTER VI 

GENERAL DEATH-RATES, BIRTH-RATES, MARRIAGE-RATES 

Gross, or general, death-rates — Precision of death-rates — 
Corrected death-rates — Revised death-rates — Variations in 
death-rates in places of different size — Errors in published 
death-rates — Rates for short periods — Birth-rates — Relation 
between birth-rates and death-rates — Fecundity — Marriage- 
rates — Divorce-rates — Natural rate of increase — Comparison 
of general rates — Marriage-rates, birth-rates and death-rates in 
Sweden — Downward trend in birth-rates and death-rates — 
Variations due to population estimates — Birth-rates and death- 
rates in Massachusetts — Monthly death-rates in Massachu- 
setts — Marriage-rates in Massachusetts — ^Divorce-rates . in 
Massachusetts — Limited use of gross death-rates — The ideal 
death-rate 186 



CHAPTER VII 

SPECIFIC DEATH-RATES 

Restriction of death-rates — Ages of Man — The vision of 
Mirza — Computation of specific death-rates — Specific death- 
rates by ages and sex — Specific death-rates as affected by mari- 
tal condition — Specific death-rates and nationality — Influence 
of age composition of population on death-rate — Influence of 
racial composition on death-rates — Chronological changes in 
specific death-rates — Fallacy of concealed classification — Use of 
specific death-rates — Death-rates adjusted to a standard popu- 
lation -^ Examples of adjusted death-rates — Adjustment of 
racial difTerences — Death-rates for particular diseases — Special 
death-rates 220 



X CONTENTS 

CHAPTER VIII 

CAUSES OF DEATH 

Nosography — Nosology — Purpose of Nosology — History of 
nosography — International list [of causes of death — Classifi- 
cation of diseases in 1850 — Present-day classification — Unde- 
sirable terms — Synonjnns of typhoid fever — Joint causes of 
death — Classification of occupations — Nosology not an exact 
science 



Page 



254 



CHAPTER IX 

* ANALYSIS OF DEATH-RATES 

Reasons for analyzing death-rates — Two methods of analysis 
— Useful sub-divisions — Analysis of the death-rate of a state — 
Comparison of death-rates of two cities — Rates not the only 
methods of comparison 299 



CHAPTER X 

STATISTICS OF PARTICULAR DISEASES 

Mortality rate — Proportionate mortality — Morbidity-rate — 
Fatality — Inaccuracies of morbidity and fatality-rates — Causes 
of death in Massachusetts — Study of tuberculosis by age and 
sex in Cambridge, Mass. — Seasonal distribution of deaths from 
tuberculosis — Chronological study of tuberculosis — Tuber- 
culosis and occupation — Tuberculosis and racial composition 
of population — Diphtheria in Cambridge, Mass. — Age sus- 
ceptibility to diphtheria — Fatality of diphtheria — Chrono- 
logical study of diphtheria — Urban and rural distribution of 
diphtheria — Statistical study of typhoid fever — ^Age distribu- 
tion of typhoid fever — Seasonal distribution of typhoid fever — • 
Chronological reduction in typhoid fever — Statistics of cancer — 
Further studies of particular diseases 308 



CONTENTS xi 

CHAPTER XI 
STUDIES OF DEATHS BY AGE PERIODS 

Page 
Infant mortality — • Some definitions — Pre-natal deaths — 
Infant mortality and specific death-rates of infants — First- 
year death-rate — Methods of stating infant mortality — Chron- 
ological reduction in infant mortality — Reasons for the de- 
creasing infant mortality — Infant mortality in different places 

— Deaths of infants at different ages — Specific death-rates' of 
infants at different ]ages — Expectation of life at different ages — • 
Infant mortality by age periods — Causes of infant deaths — The 
Johnstown studies — Other studies of the Childi-ens' Bureau — 
Infant mortality problems — '■ Maternal mortality — Childhood 
mortality — Diseases of early childhood — Proportionate mortal- 
ities during school age — Proportionate mortalities at higjj^er ages 

— Median age of persons living — Average age at death 339 

CHAPTER XII 

PROBABILITY 

Natural frequency — Coin tossing — Chance — Binomial the- 
orem — Chance and natural phenomena — Frequency curves, 
including skew curves — Frequency curves shown by summation 
diagrams — Deviation from the mean — Standard deviation — 
Coefficient of variation — Computation of coefficient from grouped 
data — Probable error — Doubtful observations — The proba- 
bility scale — Probability cross-section paper — Another use of 
probability — The frequency curve as a conception 376 

CHAPTER XIII 

CORRELATION 

Correlation — Causal relations — Correlation and causality — 
Laws of causation — Methods of correlation — Galton's coefficient 
of correlation — Example of low correlation — Correlation shown 
graphically — Correlation table — Use of mathematical formulae 

— Secondary correlation — The lag — Coefficient of correlation 
and the lag — Other secondary correlations — The epidemiologist's 

use of correlation 402 



xii CONTENTS 

CHAPTER XIV 
LIFE TABLES' 



Page 



Life tables — Probability of living a year — Mortality tables — 
Most probable lifetime — "Vie probable" — Expectation of 
life — Comparison of the three methods — Life tables based on 
living populations — Mathematical formulae — Early history of 
life tables — Recent life tables — United States Life Tables: 1910 
— A few comparisons 422 

CHAPTER XV 

A COMMENCEMENT CHAPTER 

The day after commencement — Military statistics — Army 
diseases — HKect of the war on demography — Hospital statis- 
tics — Statistics of industrial disease — List of occupations — 
Economic conditions and health — • Accidents — Age distribution 
of poliomyelitis — Averages and median age of persons living — 
Average age at death — The Mills-Reincke phenomenon — The 
sanitary index — Publication of reports 436 

APPENDIX I 

REFERENCES 

General text-books — Periodicals — Reports — Demography — 
Arithmetic — Graphics — Census — Population — Death-rates — 
Probability — Correlation — Life tables 459 

APPENDIX II 
The Model State Law for Morbidity Reports 465 

APPENDIX III 

The Model State Law for the Registration of Births and 
Deaths 472 

. APPENDIX IV 
Table of Logarithms of Numbers 491 



VITAL STATISTICS 



CHAPTER I 
DEMOGRAPHY 



Broadly speaking demography is the statistical study 
of human life. It deals primarily with such vital facts 
as birth, physical growth, marriage, sickness and death 
and incidentally with political, social, educational, religious, 
sanitary, hygienic and medical matters. In a somewhat 
narrower sense demography is used as a synonym for vital 
statistics. 

The word ''demography" is derived from the Greek 
words demos, people, and grapho, to write. It is in com- 
mon use in Europe, but is not as well known or its meaning 
as well understood in America. High authority for its 
use is found in the name of that most important triennial 
gathering of physicians and sanitarians, the International 
Congress of Hygiene and Demography. 

Demography cannot be called a science in the sense that 
it is a classified body of knowledge from which laws have 
been developed and established. But all sciences in their 
evolution go through a descriptive stage in which data are 
collected and hypotheses tested. So regarded demog- 
raphy may be called a science, — the science of human 
generation, growth, decay and death as studied by statis- 
tical methods. 

1 



2 DEMOGRAPHY 

The principal divisions of demography. — Demography 
may be said to include the following major subjects: 

1. Genealogy, which considers individual ancestries and 

personal records. 

2. Human eugenics, which considers heredity from a 

scientific standpoint, and is to a large extent the 
application of the statistical method to genealogy. 

3. The census, that is, the collection of social, political, 

religious and educational facts* concerning popula- 
tion, usually by the method of governmental enum- 
eration. 

4. Registration of vital facts, such as those concerning 

birth, marriage, divorce, sickness and death, usu- 
ally under governmental direction and by the use 
of individual records. 

5. Vital statistics, which is the application of the statis- 

tical method to the study of these vital facts. 

6. Biometrics, which includes anthropometric studies of 

human growth, stature, strength, etc 

7. Pathometrics, that is, statistical pathology, which in- 

cludes detailed studies of diseases and their rela- 
tions to the human body. These facts are obtained 
largely in hospitals, by health department labora- 
tories and by life insurance companies. 
Demography both old and new. — The word '^demog- 
raphy " has come into use during the last generation, and 
has not even now taken its proper place in the list of recog- 
nized sciences; but the gathering together of facts relating to 
human life and the expression of these facts numerically 
has been practiced from time immemorial. 

Some parts of demography are older than others. Gene- 
alogy is very old. "Adam lived an hundred and thirty 
years, and begat a son in his own likeness, after his image; 
and called his name Seth: And Seth lived an hundred and 



HISTORY. OF STATISTICS 3 

five years and begat Enos: And Enos lived ninety years 
and begat Cainau; And Cainau lived seventy years and 
begat Mahalaleel:" And so it goes on. Hundreds of 
years before Christ enumerations of the people were made 
for purposes of taxation and for other reasons, as one may 
read in the histories of Egypt, Persia, Judaea, Greece, 
Rome or China. 

Many fragmentary data relating to births, deaths and 
marriages were recorded in the old church registers of 
England. Capt. John Graunt compiled the vital statis- 
tics for the city of London in 1662, which attracted much 
attention at the time. In referring to the Great Plague 
in London in 1666 Pepys tells about the published '' bills," 
that is, the list of the dead, and gives their statistics. 

But the application of statistics and the scientific method 
to genealogy is relatively modern and so are the develop- 
ments of biometry and pathometry. Sir Francis Galton 
and Professor Karl Pearson, of England, have been leaders 
in this and may almost be said to have founded a new 
school of statisticians. 

Demography, therefore, is both an old and a new 
science. 

History of statistics. — The word ''statistics "* is nearly 
two centuries old, being first used by Gottfried Achenwall, 
who lived in Jena, 1719-1772. Before that we learn of the 
political arithmeticians in France and Italy and of Aristotle 
who used statistics in describing and comparing different 
states. The systematic publication of the details of official 
statistics owes its origin to Anton Btischvig, 1724-1793, who 
published a voluminous work on historiography and founded 
a magazine in which statistics for various countries were 
brought together and compared. Crome in 1785 published 
important Tahellen-Statistik which contained various data 
in regard to population in Germany. 



4 DEMOGRAPHY 

Many well-known scientists undertook statistical in- 
vestigations. Edmund Halley, 1656-1742, the astronomer 
who discovered the comet which bears his name, compiled 
in 1693 a series of mortality tables and calculated the ex- 
pectation of life at each age and thus laid the foundation 
for scientific life insurance. In 1713 Bernouilli, noted for 
his hydraulic studies, demonstrated a theory of proba- 
bilities which a century later, 1813, was perfected by 
Laplace in his masterly treatise ''Theorie analytique des 
probabilites." 

John Graunt, already mentioned, laid the foundations 
for vital statistics when in 1662 he wrote his remarkable 
'' Natural and Pohtical Observations upon the Bills of 
Mortality." 

In 1741 Joh. Peter Siissmilch (1707-1767) published an 
important work on vital statistics from which he attempted 
to draw some far-reaching moral deductions. He tried to 
demonstrate statistically the doctrine of the '' Natural 
Order." From the equality of the sexes at marriage (at 
birth his ratio is 21 sons to 20 daughters) he derives the 
command of monogamy. From a comparison of urban 
and rural death-rates (in cities one death to 25 to 32 per- 
sons, and in the country, one to every 40 to 45 persons) 
he censures the unnaturalness, immorality, and luxury of 
city life, '' proving statistically" that these bring down 
the wrath of God. 

With the accumulation of statistical data various di- 
vergencies began to appear. The political economists, 
headed by Adam Smith (''Wealth of Nations," 1776) and 
followed by Malthus (1804) and others, separated them- 
selves from the realm of general statistics. Hitter (1779- 
1859) led the study of geography apart. At the end of 
the 18th century the life insurance companies also drew 
away from the considerations of general populations, and, 



THE WORLD'S GREAT DEMOGRAPHERS 5 

by reason of the accumulation of their own data relating 
to deaths, began to depend upon them alone. This split- 
ting up of the general science of statistics and the multi- 
plication of the practical applications of statistics led to an 
increasing laxity in method, a condition which we have 
hardly yet outgrown. 

Quetelet, 1796-1874, aroused much enthusiasm over 
statistics as 'Hhe queen of all the sciences." His work on 
probability was justly famous and was an inspiration to 
Florence Nightingale. Since his time, however, this branch 
of the subject has been more commonly considered as a 
part of pure mathematics and is treated in books on 
^' Least Squares," the law of error, and precision of meas- 
urements. 

Finally, we come to the brilliant works of Galton, Karl 
Pearson and others, already mentioned. 

The history of statistics is a fascinating one, as it flits 
around from country to country, now flourishing in Italy, 
then in France, England, Denmark, Germany, England 
again. The United States has had many able statisticians 
but few statistical mathematicians worthy to be compared 
to Laplace, Quetelet or Karl Pearson. 

The world's great demographers. — Some of the great- 
est scientists of the world have been enthusiastic statisti- 
cians. In some cases their greatness has been due to their 
statistical skill. Even at the present time it is safe to say 
that the most successful health officers are good statisti- 
cians, although it does not follow that all good statisticians 
are successful health officers. 

The following is a short list of men, not now living, who 
have made important contributions to the study of statis- 
tics, — especially vital statistics. The student will find it 
interesting to add to this list. 



6 DEMOGRAPHY 

Capt. John Graunt (1620-1674), of England. 
Melchiorre Gioja (1767-1829), of Italy. , 
Sir Francis Galton (1822-1911), of England. 
William Farr (1807-1883), of England. 
Louis A. Bertillon (1821-1883), of France. 
Alphonse Bertillon (1853-1914), of France. 
Edwin Chadwick (1800-1890), of England. 
Florence Nightingale (1820-1910), of England. 
Edward Jarvis (1803-1884), of Boston, Mass. 
Lemuel Shattuck (1793-1859), of Boston. 
Samuel Warren Abbott (1827-1894), of Boston. 
Carroll D. Wright (1840-1909), of Massachusetts. 

Section of Vital Statistics. — The American Public Health 
Association has always manifested a keen interest in vital 
statistics. Some of the reports of its committees have had 
a far-reaching effect. In 1907 a Section of Vital Statistics 
was organized in this association, and since that date the 
journal of the association, now known as the American Jour- 
nal of Public Health, has contained many important articles 
on the subject. Membership in this section is open to regis- 
tration officials, statisticians, epidemiologists, sanitarians 
and other members of the American Public Health Associa- 
tion who are interested in vital statistics. 

The ** Statistical Method." — Statistics are facts ex- 
pressed by figures. Strictly speaking a birth reported and 
recorded officially is not a statistic, but a vital fact; yet 
inasmuch as reported and recorded births are commonly 
counted and the results expressed numerically it is appro- 
priate to regard such a birth record as a statistical unit 
or item, that is, as a statistic. It is not customary, how- 
ever, to use the word in the singular number. 

By expressing facts by figures it is possible to arrange 
them in various ways for study and comparison, as, for 
example, in tables and graphs; to classify them; to make 
generalizations; to use them in logical processes and thus 



WHY WE NEED TO USE THE STATISTICAL METHOD 7 

to draw inferences and conclusions based on the facts. 
The various mathematical processes used for this purpose 
are collectively known as the statistical method. 

Some of these processes are quite elaborate and involve 
complicated mathematical methods and conceptions, such 
as the laws of variation, dispersion, correlation and prob- 
ability. For many years there has been a discussion as 
to whether ''statistics" should be regarded as a distinct 
science, ranking with physics, chemistry and biology or 
merely as a method. Westergaard expresses the truest 
conception when he says that ''it is an auxiliary science in 
many branches of human thought." "There are some 
statisticians who are statisticians and there are some stat- 
isticians who are mathematicians." There are theories 
of statistics which comprise a very considerable part of 
mathematics. Volumes have been written on the Calcu- 
lus of Probabilities, on Least Squares, on Variation. On 
the other hand, many of the statistical processes are ex- 
tremely simple and do not get beyond the bounds of 
ordinary arithmetic. The simple processes have a wide 
general use; the more elaborate processes have their place 
but are not commonly applicable or necessary. 

Why we need to use the statistical method. — People 
who do not like mathematics often say "Oh! Pshaw! 
Why do we have to study statistics? Of what good are 
they? " The answer is that in a big world we have to 
deal with many facts and the statistical method enables 
us to abbreviate facts, to concentrate them so that we 
can more readily study and compare them and find out 
what they mean. If you want to live in a little world and 
deal with only a few facts then you do not need statistics. 
The head of a small factory may remember the wages of 
each one of his employees. Tom gets ten dollars a week, 
Fred gets twelve, Sam and Bill each get fifteen and Henry 



8 DEMOGRAPHY 

gets sixteen dollars. But the head of a large factory 
where there are a hundred hands cannot carry all these 
facts in mind. The bookkeeper of course has a record of 
them, very necessary for pay-day. The head of the fac- 
tory may know, however, that ten of the employees get 
sixteen dollars a week, fifteen get twelve dollars and sev- 
enty-five get ten dollars. The factory superintendent 
needs these statistics. He lives in a large world. The 
village gossip knows the dates of all the births, marriages 
and deaths in town since January first, but she lives in a 
little world. To^^compare these facts with similar facts 
for the next town and the one next to that requires that 
the facts be expressed in figures. Statistics enable one to 
enlarge his horizon. 

Why are statistics thought to be **dry"? — Statistics 
have the popular reputation of being dry, uninteresting, 
or, as Shakespeare would say, — ''flat, stale and unprofit- 
able." This is very natural,- for all figures look alike. If 
we are considering one hundred and thirty-seven tons of 
coal we use the figures 137 and if we are talking about the 
same number of American Beauty roses we also use the 
figures 137. If we think only of the figures we see no 
difference between these statistics. It does not take 
much imagination to visualize 137 roses, their beauty and 
their odor; it takes more, perhaps, to visualize 137 tons of 
coal. And if 37 of the roses are said to be yellow, 60 
white and 40 red, we can visualize the whole mass even 
if we know that they are mixed. The reason why statis- 
tics are ''dry" is because people do not try to visualize 
them. If you don't try to visualize the statistics the 
figures are commonplace and of course uninteresting, while 
if you do try the mental effort is tiring. Moreover, there 
is a real difficulty and that is our inability to visualize 
very large figures. I may be able to visualize a hundred 



CAN ONE PROVE ANYTHING BY STATISTICS 9 

dollars, but I confess not to be able to visualize a million 
dollars, even though I know that it is one thousand times 
as much as one thousand dollars. Also visualization is 
lost, or at any rate confused, when we begin to perform 
mathematical operations with our statistics. 

The way to prevent statistics from being ''dry '^ is to 
keep in mind that statistics are not merely figures, but are 
figures which stand for facts. 

Is it true that " you can prove anything by statistics " ? 
— We often hear it said ''Oh! you can prove anything by 
statistics." Is this true ? Suppose we substitute the mean- 
ing of statistics and say "you can prove anything by 
facts if expressed in figures." Obviously this is not so. 
Facts are facts whether expressed in figures or not. If 
the conclusions are wrong the trouble lies not in the sta- 
tistics but in the way they are used. The drawing of con- 
clusions is the function of logic, a process of reasoning, 
and fallacious reasoning should not be charged against 
statistics. 

And yet there is something which underlies the popular 
statement. When figures are used to express facts, and 
when the logical processes are applied to figures, divorced 
in the mind from the facts for which they stand, it is easy 
for fallacies to creep in without being recognized; it is 
easy to compare things which ought not to be compared, 
to generalize from inadequate data, and to commit all sorts 
of illogical errors. Thus the unscrupulous may fool the 
unwary, and the innocent may fool themselves. Hence 
to use statistics properly one must be able not only to 
visualize the facts but to think logically. Students who 
would be statisticians should therefore 'study formal logic. 
Some of the common fallacies in the use of statistics will 
be considered on later pages. Honesty and conservatism 
are essential qualities for the makers and users of statistics. 



10 DEMOGRAPHY 

There are numerous works on logic. One of the best is 
''The Principles of Science," by W. Stanley Jevons. It 
treats not only of logic but of the scientific method in 
general. 

The national value of ** Vital Bookkeeping." — It is of 
the greatest importance to a nation that accurate records 
be kept of its vital capital, of its gains by birth and immi- 
gration and of its losses by death and emigration, for a 
nation's true wealth lies not in its lands and waters, not in 
its forests and mines, not in its flocks and herds, not in its 
dollars, but in its healthy and happy men, women and 
children. A well man is worth more to a nation than a 
sick man ; ai man in the prime of life is of more immediate 
worth than an old man or a child, a married man is poten- 
tially a greater asset than a single man. Hence, in a na- 
tion's vital bookkeeping the number of people, their age 
and sex and conjugal condition, their parentage, their 
health, the rate of births and deaths, are matters of great 
moment. Their environment is also important; their con- 
centration in cities and villages and congested areas, their 
mode of housing, their occupation, their state of intelli- 
gence, their economic condition, their knowledge of sani- 
tation, all contribute to the sum total of their usefulness 
to themselves and to society. 

Vital bookkeeping is carried on much as ordinary book- 
keeping; there are daily entries of accessions and losses as 
they occur, corresponding to receipts and payments; there 
are weekly statements, monthly statements and annual 
statements; and at longer intervals there is a taking 
account of stock, that is, a census. One important differ- 
ence, however, sho'uld be noted. Accounts are accurate 
records of transactions and if properly kept an exact bal- 
ance will be obtained Vital statistics are not always 
accurate, the individual data are incomplete and subject 



STATISTICS NECESSARY FOR HEALTH OFFICER 11 

to error; the results, therefore, lack the precision of mone- 
tary accounts. It is necessary to keep this fact constantly 
in mind when interpreting the results of statistical studies. 
An understanding of the principles of the arithmetic of 
inexact numbers and of the theory of probability is essen- 
tial. 

Vital statistics are useful for many purposes. To the 
historian they show the nation's growth and mark the 
flood and ebb of physical life; to the economist they in- 
dicate the number and distribution of the producers and 
consumers of wealth; to the sanitarian they measure the 
people's health and reflect the hygienic conditions of the 
environment; to the sociologist they show many things 
relating to human beings in their relations one with another. 

Vital statistics necessary for health officer. — Vital sta- 
tistics are not to be collected and used as mere records of 
past events: an even more important use is that of prophe- 
sying the future. An engineer in planning a water supply 
to last for a generation estimates the future population by 
the previous rate of growth; so also in laying out a system 
of streets and sewers and transportation service. The 
whole idea of city planning is fundamentally based on the 
use of the vital statistics of what has been as a means of 
estimating what is to be. 

The health officer of a city or he whose duty it is to col- 
lect and record the vital statistics should study them as 
soon as received and not wait until some convenient day 
when other work is slack and then merely tabulate and 
make averages for formal reports and permanent records. 
Vital statistics, especially those of morbidity, should be 
studied in the making, and just as the meteorologist reads 
his instruments daily in order to forecast the weather and 
give warnings of the coming hurricane, so the efficient 
health officer will daily study the reports of new cases of 



12 DEMOGRAPHY 

disease in order that he may be forewarned of an impend- 
ing epidemic and take measures to check its ravages. 

No Ughthouse keeper on a rocky coast is charged with 
greater responsibihty than he who is set to watch the 
signs of coming pestilence from the conning tower of the 
health department. Making another comparison, we may 
say that the health service should be organized for rapid 
work like a fire department,' with its rapid facility for 
learning that a fire exists and its ever ready apparatus for 
extinguishing the blaze. If the fire alarm is not rung, 
the blaze will spread, and if cases of disease are not reported 
the epidemic will likewise spread. The duty of reporting 
cases of infectic^s disease rests upon the practicing physi- 
cians, and thereby hangs a sad and discouraging tale. 

National vital statistics. — It has now become well rec- 
ognized that the maintenance of accurate records of vital 
statistics is a proper governmental function, and no nation, 
state or city can be considered as having a complete gov- 
ernmental equipment which does not provide for the 
proper collection and permanent record of such statistics. 
But, as will be seen, even our longest governmental rec- 
ords are relatively short, and for that reason we should 
be careful in drawing general conclusions from them. 

Sweden, — Of modern nations Sweden has a just claim 
to the longest unbroken series of vital statistics. In 1741 
registration of births, marriages and deaths was begun in 
all parishes and since 1749 a census has been taken each 
year. The principal data for this long period (1750-1900), 
were given in a most valuable paper by Sundbarg at the 
International Congress of Hygiene and Demography in 
Berlin in 1907. 

France. — In 1790 Lavoisier (1743-1794), after the 
French Revolution, collected extensive data relating to 
the population of that country, the amount of land under 



NATIONAL VITAL STATISTICS 13 

cultivation, etc., but the first actual enumeration of the 
inhabitants of Paris was not made until 1817. 

England. — In England the old parish records date back 
at least to 1538, when Henry VIII ordered all parsons, 
vicars and curates to keep true and exact records of all 
weddings, christenings and burials. It was not until 1801 
that a national census was taken, and it was not until 1851 
that a complete census was made. 

United States of America. — America is far behind other 
civilized countries in its records of vital statistics. There 
is no national registration system, no complete national 
record of births and deaths. This results from our dis- 
tributive form of government, the control of such matters 
being a state or municipal function, not a federal one. 
The records vary greatly in different parts of the country. 
Some of the older states like Massachusetts and New 
Jersey possess fairly accurate records that extend back for 
several decades, but in some of the western and southern 
states the records are either absent or so incomplete as to 
be worthless. At the time of the last census, in 1910, the 
registration area where the death records were considered 
accurate enough to warrant their being published included 
only 58 per cent of the total population of the country. 
This condition of affairs may be charitably regarded as a 
youthful sin of omission, but if it is much longer contin- 
ued it will be nothing less than a national disgrace. The 
health statistics of our best administered cities are much 
inferior to the published vital statistics of European cities, 
as, for example, those of Hamburg, Germany. The United 
States Census Bureau, now permanent, has become in- 
creasingly efficient in recent years, and its reports are of 
much value, but not until a centralized public health serv- 
ice has been secured will the nation's vital statistics be put 
upon a high plane of comprehensiveness and accuracy. 



14 DEMOGRAPHY 

The importance of statistical induction. — In using sta- 
tistics we necessarily employ the methods of logical think- 
ing comprised in what is termed 'induction," methods by 
which general tendencies and laws are drawn out of accu- 
mulations of facts. 

Statistical induction may be said to be one of the most 
potent weapons of modern science. Referring to it Royce 
says that the technique of statistical induction consists 
wholly in learning how to take fair samples of the facts in 
question, and how to observe these facts accurately and 
adequately. 

Statistics are being constantly invoked for testing hy- 
potheses in all branches of science. This involves four 
distinct processes, — first, the choice of a good hypothesis; 
second, the computation of certain consequences, all of 
which must be true if the hypothesis is true; third, the 
choice of a fair sample of these consequences for a test; 
fourth, the actual test of each of these chosen hy- 
potheses. 

Deductive reasoning as well as inductive reasoning is 
involved in the use of vital statistics. It is perhaps the 
natural order of mental processes for the mind pursuing 
an inductive study to leap ahead to some conclusion and 
then fill in the intervening steps by working backward by 
deduction. 

It is by the application of the principles of logic that 
the statistician is able to keep his conclusion within rea- 
sonable bounds. 

Choice of statistical data. — First, there is the complete 
statistical study which includes a full count of all the units 
within the desired area or within the specified time. This 
method, of course, brings the surest results, but it is often 
impossible. Second, is the monographic method, a pro- 
cedure in which a detailed and exact study is made of a 



EXERCISES AND QUESTIONS 15 

particular group. Where the group selected for study is 
a well-chosen type the application of this method yields 
valuable results but there is danger in generalizing from 
monographic researches. The third method is the repre- 
sentative method, a study of certain selected parts repre- 
sentative of the whole. This is analogous to the method 
of the analytical chemist where chosen samples are analyzed 
and the results applied to the whole. The value of this 
method depends upon the accuracy of the sampling process 
quite as much as upon the enumeration of the facts em- 
braced by the sample. The representative method is 
widely used. There are two general methods of sampling. 
One is that of random selection, the other is that of mix- 
ture and subdivision. The object in both cases is the same, 
— to secure a sample truly representative of the whole. 
The tendency to take samples of the obvious and the 
accessible is one that must be constantly struggled against. 

EXERCISES AND QUESTIONS 

1. How can vital statistics be used to determine relative values in 
public health activities? [See Am. J. P. H., Sept., 1916, p. 916.] 

2. Describe the common method used in compihng genealogies. 
[Consult some systematic genealogy, — say that of your own 
family.] 

3. Prepare a diagram of your own ancestry, giving the names of 
your father and mother, the dates of their birth (and death) and their 
birthplaces; also the same information as to your two grandfathers 
and your two grandmothers; your four great-grandfathers, etc, as far 
as the information can be readily obtained. 

4. Who was Mendel and what is the Mendelian law? [See Rose- 
nau's Preventive Medicine and Hygiene, Chapter on Heredity and 
Eugenics.] 

5. What are the primary laws of heredity and eugenics? 

6. What information can you give as to the heights of your father and 
mother, your grandfathers and grandmothers? Can you illustrate any 



16 DEMOGRAPHY 

of the laws of heredity, as to height, color of hair or any other char- 
acteristics, from your own family records? 

7. Can you suggest a schedule of anthropometric data to be kept for 
each person as a matter of f amUy record? 

8. Write a short biographical sketch of some person famous for work 
in statistics, demography or vital statistics. (Name to be assigned 
by the instructor.) 



CHAPTER II 

STATISTICAL ARITHMETIC 

Statistical processes. — The principal processes used in 
the study of vital statistics are these: 

Collection of the facts: 

Classification of the facts. 

Generalization from the facts. 

Comparison of the facts. 

Drawing conclusions from the study of the facts. 

Display of the facts. 

Collection of data. — There are two primary methods of 
obtaining the data needed in demography — enumeration 
and registration. In the first case the statistician goes or 
sends to get the facts. The persons employed are enumer- 
ators or inspectors. This is the method of census taking 
and is described in another chapter. In the second case 
the facts are reported to the statistician in accordance with 
established rules and regulations. For example, physicians 
and undertakers are required to send notices of deaths and 
burials to the proper authorities. Some of the methods 
in common use and the laws which govern the reporting of 
vital facts are described later on. 

It is of vital importance to make sure that the data 
collected are sufficient in kind and number for the purpose 
for which the statistics are intended. It saves time and 
labor in the end to consider carefully at the outset just what 
data are needed. Where, as is often the case, the statis- 
tician has no control over the collection of the data, he 

17 



18 STATISTICAL ARITHMETIC 

should make every possible attempt to ascertain the reliabil- 
ity of the sources of information and not attempt to draw 
conclusions not warranted by the conditions under which 
the figures were collected. 

Statistical units. — The basic statistical process is count- 
ing. An easy process, — one says ; and so it is if we know 
what to count, and if we know what to include and what to 
leave out. Here at the very outset we meet our first diffi- 
culty. 

Before going on stop and define a '^ dwelling-house." 
Is a church a dwelling-house if the sexton lives in it? Is 
a garage a dwelling-house if the chauffeur lives in the sec- 
ond story? Is a building with two front doors one dwell- 
ing-house or two? Is a '' three-decker " one dwelling-house 
or three? Or try to define an infant, a birth, a cotton-mill 
operative or any other unit used in demography. 

Statistical units are the things counted and represented 
by numbers. Obviously every fact, every item, counted 
must be included within the definition of the unit. No 
part of a statistical study demands more careful study than 
the definition of the statistical units to be employed. 
Each unit should not only be rigidly, accurately and in- 
telligibly defined, it should be steadily adhered, to during 
the investigation. This is by no means easy. 

In counting the number of deaths in a city should non- 
residents be included? Should still-births be included in 
'^ births"? Has practice in this matter been constant 
during the last fifty years? Has pneumonia always meant 
what it means to-day? And what has become of the causes 
of death which no longer appear on our lists? It is cer- 
tainly obvious that all statistics relating to the causes of 
death must be used with the utmost caution, and this is 
especially the case if the statistics cover a considerable 
period of time. 



ERRORS OF COLLECTION 19 

Or, let us take the simple matter of age. What is a 
seven-year old child? Shall we take the nearest birthday, 
or the last birthday? Or shall we do as is done in some 
foreign countries and take the next birthday? In the latter 
case a child at birth is regarded as of age one. Even the 
United States census has not always followed the same 
method of ascertaining age. 

Errors of collection. — One of the errors of enumeration 
is failure to find the units to be counted. In taking a 
census some persons are never found by the enumerators. 
They may be accidentally missed, or they may be traveling, 
away from home or hiding. At the last census in England, 
where the data are collected on a single day, it is said that 
some of the suffragettes walked the streets for the entire 
period, so as not to be at home when the enumerators 
called, arguing that if they could not vote they ought not 
to be counted. Failure to obtain complete records is still 
greater when the data are obtained by registration. 

The opposite error sometimes occurs, namely over-regis- 
tration. This is usually due to carelessness, but padded 
censjus records have been known to occur. 

There are two kinds of errors which need to be distin- 
guished — balanced errors and unbalanced errors. For ex- 
ample, if a thermometer is correct it may be assumed that a 
good observer will be as likely to read too high as too low 
and that in a long series of readings the errors will balance 
each other. But if the thermometer is at fault all of the 
readings will be too low or too high, that is, the errors will 
be unbalanced. Causes of unbalanced errors must be re- 
moved if possible or, if not removed, the results must be 
corrected for them. 

In recording such quantities as the height and weight of 
persons the errors may be regarded as balanced, but physi- 
cians in reporting diseases may by their practice of diagnosis 



20 STATISTICAL ARITHMETIC 

introduce unbalanced errors. Again, the aggregation of 
the records of various physicians may cause these errors to 
become more or less balanced. 

Finally we have the effect of the personal equation of the 
collector. His mind may have certain grooves through 
which errors creep into his work. If reading a scale he may 
have a natural tendency to over-estimate the space between 
divisions, — if counting units he may have a natural tend- 
ency to skip some. What is more serious, he may possess 
the unpardonable statistical sin of carelessness, or worst of 
all, he may be dishonest. Ignorance and failure to under- 
stand the definition of the units that are to be enumerated 
are also fruitful sources of error. 

Tally sheets. — When many items are to be counted, and 
especially when there are different units which must be 
kept apart it is convenient to use some form of tally sheet. 
Each item is first indicated by a line or a dot and these are 
afterwards counted. There are two common methods — 
the cross-five method and the cross-ten method. In the 
former every fifth item is indicated by a line which crosses 
four, making a group of five. In the latter nine items are 
indicated by dots, the tenth by a cross over the dots. Other 
devices will doubtless suggest themselves to the reader. 
(Fig. 1). 

. Tabulation. — For purposes of study and display the 
collected data are commonly arranged in tabular form, 
that is in columns and lines. The preparation of tables is 
an important part of statistical work and cannot be done 
too well. The object of a table is to bring statistics to- 
gether for comparison, to condense information. Essential 
qualities of good tabular work are clearness, compactness 
and neatness. Tables are expensive to print, hence the 
most should be made of each one. The following sugges- 
tions, if followed, should yield good results: 



TABULATION 



21 



1. Each table should have a title which tells clearly 
what the table contains. Preferably the title should be 
short, but clearness is the main thing. It is excellent train- 
ing in the use of words to produce an artistic title. 



THE CROSS FIVE METHOD 



Disease 


Number 


Measles 


lUV /AV /AV // /7 


Scarlet-fever 


//// /// 8 


Whooping-cough 


UH U^ LW U^ ZO 



THE CROSS TEN-METHOD 



Disease 


Jan. 


Feb. 


Mar. 


Apr. 


May 


June 


Etc. 


Me^es 


•J 


% 


:'<?: 


•f 


•(S- 


■/ 




Scarlet-fever 


X 


■/ 


s 


•:^; 


(9 


Z 








Whooping-cough 


•*(• 


^ 


^ 


:•• 


• • . 




•^ 


... 


M^ 


•.:■■ 








2 





/ 


f 




1 


/ 


? 


W.^ 


6 

































































Fig. 1. — Tally Sheets. 



2. Each column should have a clear and appropriate 
heading. As the space for the heading is often small ab- 
breviations may be used, provided they are well understood 
or well explained in the accompanying text. 

3. If the heading is complex, that is, if certain parts of 
the heading cover more than one column, care should be 
taken to have this clearly indicated by proper rulings.. 



22 STATISTICAL ARITHMETIC 

Printers call this " boxing." If there are few columns and if 
the headings are simple, the rulings are unnecessary. 

4. If the different columns of a table are likely to be j:e- 
ferred to in the text it is convenient to have each column 
given a serial number from left to right, placed in paren- 
thesis just below the heading. 

5. Long unbroken columns of figures are confusing to the 
eye; especially if the figures of different columns are to be 
compared on a given line. This trouble can be obviated by 
leaving horizontal spaces between every few lines or by the 
use of horizontal rulings. Sometimes, for purposes of 
reference, each line is given a serial number from top to 
bottom. 

6. The columns of a table should not be widely separ- 
ated even if there are only a few columns and the page is 
large. Compactness is a virtue. Much paper is wasted in 
annual reports by badly arranged tables. On the other 
hand the type used in tabular work should not be too 
small. 

7. If the figures tabulated have more than three signifi- 
cant figures it is a good plan to separate them into groups 
of three. Thus, we should not write 6457102, but 6 457 102. 

Tables 1 and 2 are given as examples of tabulation and 
boxing. From this point on students should criticize the 
tables in this book (a few of which have been intentionally 
made imperfect), and they should use great care in the prep- 
aration of every table involved in the ^' Exercises and Ques- 
tions." 



TABULATION 



23 



TABLE 1 
CAMBRIDGE, MASS. 
Estimates of Population 



Census. 



(2) 



Estimate 
based on 

U. S. 
census. 



(3) 



Estimate 

based on 

U. S. and state 



(4) 



Estimate 

based on 

local data. 



(5) 



Estimate 

used by 

local board 

of health. 



(6) 



Estimate 

used in 

this report. 



(7) 



24 



STATISTICAL ARITHMETIC 



TABLE 2 
CAMBRIDGE, MASS.: BIRTH-RATES 





Population 

estimate. 


Number of Births. 


BuiJ;i-rate. 


Year. 


Total. 


Resident. 


Gross. 


Resident. 


As stated 
by, etc. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 












• 





Inexact numbers. — In vital statistics we are usually 
compelled to deal with data ^ which are not strictly accurate. 
The figures used to express the results, therefore, should be 
prepared with this fact in mind. Unnecessary figures 
should be omitted and only those digits should be included 
which are supported by the data. Two guiding principles 
should be followed in making numerical statements of 
data; — first, to have the figures of the compilation depend 
upon and indicate the accuracy of the observations; and, 
second, to carrj^ the final numerical result no further than 
practical use demands. 

Let us take as an illustration the result of the U. S. 
Census of 1910, according to which the population of the 

1 Do not misuse this word. It is a plural word. The singular num- 
ber is "datum," but this is seldom used. Do not say, "The data 
is . . . ,"but " The data are. ..." 



INEXACT NUMBERS 25 

country is stated as 91,972,266. Obviously this figure 
cannot be strictly true. Let us suppose the possible error 
to be as much as 200,000. We might write the result '' 92 
milhon"; but this would be needlessly crude, though accu- 
rate enough for some purposes. We might say that the 
population was between 91.8 and 92.2 million, or we 
might write 92,000,000 ± 0.2 per cent. The U. S. Census 
Bureau publishes the figures as collected, leaving it for 
him who uses the figures to abbreviate them into round 
numbers according to the use which is to be made of 
them. 

Experience has shown that very few measurements or 
observations of anything are accurate to five significant 
figures, many not to three, and some are doubtful in the 
second figure. 

In tabulating the results of original data it is best to give 
the figures as obtained. But in discussing the results it is 
better to use round numbers, the number of significant 
figures depending on the accuracy of the data and the needs 
of the problem at hand. 

In presenting figures orally to an audience it is especially 
important to use round numbers. Nothing is more dead- 
ening than for a speaker to tire the ear with the reiteration 
of meaningless digits. 

Example. — Let us suppose that the number of bacteria 
on a plaj^e can be counted within five per cent, plus or minus, 
and that three different tests gave the following numbers: 
— 2790, 4220 and 3470 per c.c. the average being 3493. 
Five peV cent of this figure is 175; — hence the true result 
might conceivably lie between 3318 and 3668. Obviously 
it would be sufficiently accurate and for many reasons 
better to state the result as 3500 per c.c. Recognizing these 
unavoidable errors in our present methods the Committee 
on Standard Methods of Water Analysis of the American 



26 



STATISTICAL ARITHMETIC 



Public Health Association has suggested that statements of 
analysis should be limited in significant figures as follows: 
Unfortunately the rule has not been lived up to. 

TABLE 3 

RULE FOR STATING THE RESULTS OF BACTERIAL 
COUNTS IN WATER ANALYSIS 



Numbers of bacteria found. 


Records to be made. 


Ito 


50 


As found . 


51 to 


100 To the nearest 5 


101 to 


250 


10 


251 to 


500 


' ■' " 25 


501 to 


1,000 


' " " 50 


1,001 to 


10,000 


100 


10,001 to 


50,000 


' " " 500 


50,001 to 


100,000 


' '' " 1,000 


100,001 to 


500,000 


' *' " 10,000 


500,001 to 


1,000,000 


' " " 50,000 


1,000,001 to 10,000,000 


100,000 



Perhaps, sometime, demographers will prepare a similar 
table for the use of round numbers in vital statistics. 

Vital statisticians should at least endeavor to follow the 
example of the bacteriologists and by concerted action cut 
out fictitious accuracy from their reports. 

Precision and accuracy. — Numerical statements of 
measurements are accurate as they approach the true value 
of the thing measured; they are precise as they approach 
the mean of the measurements. Accuracy takes into ac- 
count unbalanced as well as balanced errors; precision is 
concerned with balanced errors only. It is possible for 
results to be precise and yet be erroneous. 

Combinations 6f inexact numbers. — When data which 
differ in precision are combined it is possible that faults 
may be obscured. Let us take the case of a simple addi- 
tion of the three items in column (1). 



RATIOS 



27 



TABLE 4 
EXAMPLE OF COMBINATION OF INEXACT NUMBERS 



Item. 


Percentage error. 


Possible error in item. 


(1) 


(2) 


(3) 


47,386 
9,453 

843,782 

Sum 900,621 


2 

5 
0.5 


± 948 
± 473 
±4219 

±5640, or 0.6% 



The true value of the sum may he between 895,000 and 
906,000. The result may be written, therefore, 900,000 
± 0.6 per cent. The percentage error of the sum would 
not, of course, be the sum or even the average of the figures 
in the second column. 

Ratios. — The ratio between two numbers may be ex- 
pressed as a common fraction or may be indicated by the 
ratio sjrmbol, the colon (:). Thus we may write | or 4 : 8. 
If the figures are small the difference between the two num- 
bers can be visualized, but if they are large, as for example 
^fl, or 165 : 217, it is difficult to appreciate their meaning. 
If common fractions are used to indicate ratios they should 
be limited to those in which the denominator is below 10, 
or is some round number, such as a multiple of 5 or 10. 
Thus we might speak understandingly of a J or a | or a ^V or 
a ^^jj, but not of a yV oi" a 2^3^- 

For most purposes in statistical work decimal fractions are 
to be preferred to common fractions. They facilitate print- 
ing as they occupy only one line and do not require the use 
of smaller type. It must never be forgotten, however, that 
a decimal fraction is composed of two parts, just as a com- 
mon fraction, namely the figures which are printed and 



28 



STATISTICAL ARITHMETIC 



unity (or one) which is not printed. 



Thus ^ = ^^ = 0.75. 
4 1 



A decimal fraction is therefore just as much a ratio as a 
common fraction. 

In statistical work we are constantly obliged to compare 
facts on the basis of their ratios. Let us suppose that we 
desire to compare cases and deaths from typhoid fever in 
three different places and that the data are as follows: 

TABLE 5 



Place. 


Cases. 


Deaths. 


(1) 


(2) 


(3) 


X 
Y 
Z 


541 
672 

247 


46 
53 
30 



In order to make the comparison we must select either one 
or the other quantity as a base, either cases or deaths. 
If we select one death as the unit base we have the following 
ratios : 

TABLE 6 



Place. 


Number of cases to one death. 


(1) 


(2) 


X 
Y 
Z 


11.8 i.e. 541 -r- 46 

12.7 672 -=- 53 

8.2 247 -T- 30 



If we select one case as the unit base we have the follow- 
ing ratios, expressed as decimals: 



RATES 



29 



TABLE 7 



Place. 


Number of deaths to one case. 


(1) 


(2) 


X 
Y 
Z 


0.085 i.e. 46^541 
0.079 53-^672 
0.121 30^247 



We might however select 100 cases as the base unit, in 
which case the figures are 100 times as large and we have 



TABLE 8 



Place. 


Per cent of 

cases which 

resulted in 

death 


(1) 


(2) 


X 
Y 
Z 


8.5 

7.9 

12.1 



Rates. — Now rates are merely ratios referred to some 
round number as a base. When 100 is used as the base we 
have a percentage rate, that is a rate per one hundred; 
but we may use 10 or 10,000 or even 100,000 or 1,000,000 
as the base, and very often do so. In many cases we use 
one as the base. Thus we speak of " gallons of water per 
day," meaning the number of gallons of water for one day, 
the ''number of persons per square mile," meaning, of course, 
one square mile. All of these rates, where only two quan- 
tities are compared may be called simple rates. Simple 
rates have onlj^ one base. 

Compound rates are those which have two bases. Thus 
we speak of " gallons of water per capita per day," meaning 



30 STATISTICAL ARITHMETIC 

the number of gallons of water used by one person in one 
day. The '' number of births per 1000 marriages per 
annum " would also be a compound rate. Most of the 
rates used for comparison in vital statistics are compound 
rates as they involve both number and time, the latter 
often being understood as one year, the calendar year per- 
haps. 

Misuse of rates. — Fictitious accuracy in the use of 
rates and ratios should be avoided. If 35 out of 57 balls 
were white the percentage of white balls would be 61 404 
per cent. The smallest possible error, i.e., 1, would change 
the percentage to 59.65 per cent or 63.16 per cent. To use 
two or even one place of decimals is here absurd. Clearly 
for figures less than 100 fractions of per cents are illogical. 
In the same way death-rates for populations of less than 
1000 are useless beyond the third significant figure. Com- 
parisons of averages of fictitious values are also to be avoided. 

Changes of base in the computation of rates should be 
kept in mind in order to avoid error of statement. Here 
is a well-known illustration: In the year 1880 the receipts 
of a water company were $400,000; between 1880 and 1890 
they increased 10 per cent, that is, they became $440,000; 
between 1890 and 1900 they decreased 10 per cent, that is, 
they became $396,000 (not $400,000). It is said that a 
strike once resulted from this fallacy. A company found it 
necessary to reduce wages 20 per cent for a certain period, 
promising to raise the wages 20 per cent at the end of the 
period. Naturally the men who were reduced from $2.00 
a day to $1.60 thought they would have their pay restored 
to $2.00 but found that the company wished to give only 
$1.60 + 20 per cent or $1.92. The base used should be 
stated in words if it is not perfectly clear from the context. 

When interpreting ratios it should be carefully noted 
whether or not the numerator bears a direct relation to the 



INDEX 31 

denominator. In proportion as it fails to do so any infer- 
ence from it is less valuable. The ratio between the num- 
ber of births and the total population is less close than that 
between the number of births and the number of married 
women of child-bearing age. 

Ratios are sometimes necessarily used in an indirect way. 
Thus the average annual exports and imports are taken to 
represent the business condition of a country. Here, a 
part is taken for the whole. The method is proper if, in 
the interpretation, it is recognized that it is a part. Or the 
typhoid fever death-rate of a city is taken as an index of 
the sanitary quality of the public water supply. It may 
indeed be such an index, but it is not the only one. 

In the same way crude death-rates based on total popu- 
lation regardless of sex or age are less useful in studying 
relative hygienic conditions than when these factors are 
taken into account. 

Index. — When it is not possible to find a simple direct 
ratio between two quantities, it is sometimes possible to 
combine several ratios which taken together give a better 
indication of the conditions than any one ratio used alone. 
Thus the prices of various standard commodities sold in 
any one year may be combined to give a single figure which 
will indicate the state of trade during that year. This 
combined result compared with a similar result for the 
following year will enable one to compare the state of trade 
in the two years. When several quantities are thus com- 
bined the result is called an Index, or an Average Index. 
Obviously there are various ways in which a combination 
may be made. Sometimes the weighted average of several 
quantities is used. 

The index has not come into use to any extent in the 
study of vital statistics, but it would seem logical to use it 
in comparing the relative hygienic conditions of different 



32 STATISTICAL ARITHMETIC 

cities. This is partially accomplished when crude death- 
rates are ''corrected" or adjusted to take into account 
the composition of population as to age, se^ and nation- 
ality. 

Some attempts to compute a satisfactory sanitary index 
will be referred to later on. 

Computation of Rates. — The computation of a death- 
rate for a city is merely an example in long division. As 
most health officials and some college students will have 
forgotten their arithmetic by the time they read this book 
a few words as to computation may be pardoned. The 
computation sheet should show a record of what has been 
done and should bear the date and the name or initials of 
the computer. 

Let us suppose that in a city of 34,691 people, as shown 
by the census of 1910, the number of deaths in that year was 
549; what was the death-rate per thousand of population? 
In the first place how many thousands of population were 
there? Answer, by pointing off three places, 34.691. All 
that is necessary then is to divide 549 by 34.691. This 
may be done in several ways 

The operation of long division may be done in full, thus : 

34.691)549.000(15.82 = death-rate per 1000. 
34691 
202090 
173455 



286350 

277528 



88220 
69382 



If we are content to be a little less accurate we may 
shorten the work by leaving off one decimal of the popula- 
tion, thus: 



COMPUTATION OF RATES 33 

34.69)549.00(15.82 = Answer 
3469 
20210 
17345 



28650 
27752 



8980 
6938 

The result is not changed. If we write 34.7 instead of 34.69 
we shall get 

34.7)549.0(15.82 = Answer 
347 
2020 
1735 




Still no change. Suppose we try 35 as a round number 
for the population instead of 34.7 or 34.69 or 34.691. We 
then get 

35)549(15.7 = Answer 
35_ 
199 
175 

240 

245 

This is evidently incorrect in the decimal. We have gone 
too far in using a round number for the population. 

By using discretion in omitting decimals from the popu- 
lation divisor much work maj/ be saved. It is pitiful, to see 
the energy and time wasted by some health officers in using 
unnecessary decimals in performing long-division opera- 
tions, especially as there are so many labor-saving devices 



34 STATISTICAL ARITHMETIC 

available. An easier way is to use a table of logarithms, 
and a still easier way is to use a slide-rule, a mechanical 
device for applying logarithms where approximate results 
will suffice. 

The desirable degree of accuracy of death-rates is dis- 
cussed on a later page. 

Logarithms. — Of course you have forgotten how to use 
logarithms. Let me remind you. 

If you multiply 10 by 10 you get 100. You have put 
two tens together, and you might write them thus 10^ and 
say that 10^ = 100. If you put three tens together you 
get 1000. So that 10^ = 1000. And so on. Now, ten is 
the base of logarithms, and we say that the log (meaning 
logarithm) of 100 is 2, because 2 tens multiplied together 
makes 100. And the log of 1000 is 3 and the log of 1,000,000 
is 6. So also the log of 10 is 1, the log of 1 is 0, and the log 
of 0.1 is minus 1, i.e., — 1, and so on down. Now if the 
log of 10 is 1 and the log of 100 is 2, what is the log of 20?. 
It is between 1 and 2; it is 1 plus something. Just what 
this something is you can find from a table of logarithms. 
A short table (five places) gives for the log of 2 the figures 
.30103, so that the log of 20 is 1 plus .30103, or 1.30103. In 
the same way the log of 200 is between 2 and 3; in fact 
it is 2.30103. And so we can find the logarithm of any 
number, taking the decimal from the printed table, and 
putting down the figure to the left of the decimal point 
according to the size of the original figuie, remembering 
that for figures 

Between and 10, the log is 

10 '' 100, '' 1 

100 '' 1000, '' 2 • 

1000 '' 10,000, '' 3 



THE SLIDE-RULE 35 

We use those logarithms in this way. Suppose we wish 

to multiply 100 X 10,000. We might do this in the 

regular way, 

10,000 
100 
1,000,000 = Answer. 

But the log of 100 is 2 and the log of 10,000 is 4. If we 
add these logarithms we get 6, and 6 is the log of our answer. 
That is by adding the logs of two number, the sum will be 
the log of the product of the numbers. 

And also if we subtract the log of one number from the 
log of another the difference will be the log of the dividend 
obtained by dividing the second number by the first. Thus 
in our death-rate problem the log of 549 is 2.739572 and 
the log of 34.691 is 1.540216. Hence, 

2.73957 
1.54022 
1.19935 is the log of 15.82 = the answer. 

It must be remembered that the logarithm table contains 
only the decimals. That is we look up the number which 
corresponds to the decimal .199356 and find the figures to 
be 1582. The whole number of the log being 1 tells us that 
the result is between 10 and 100, and therefore must be 
15.82. 

In this way the use of logarithms may save the statis- 
tician much time. 

A table of logarithms of numbers from 1 to 1000, carried 
to five decimal places, may be found in the Appendix. 
Tables in which there are six or seven places of decimals 
can be purchased and are in comrrion use. 

Those who do not feel confidence in themselves in using 
logarithms should consult a textbook of algebra. 

The slide-rule. — The slide-rule is a mechanical device 
for adding and subtracting the logarithms of numbers, 



36 



STATISTICAL ARITHMETIC 



and therefore it enables one to multiply the numbers for 
which the logarithms stand. It does not add or subtract 
the numbers themselves. 

In using the slide-rule it is first necessary to understand 
the scale. The logarithms of the numbers from 1 to 10 are 
as follows: 

TABLE 9 
LOGARITHMS OF NUMBERS: 1 TO 10 



Number. 


Logarithm. 


Number. 


Logarithm. 


(1) 


(2) 


(3) 


(4) . 


1 
2 
3 
4 
5 


0.00000 
0.30103 
0.47712 
0.60206 
0.69897 


6 
7 
8 
9 
10 


. 0.77815 
0.84510 
0.90309 
0.95424 
1.00000 



and above 10 the decimals repeat themselves, thus 



20 
30 



1.30103 
1.47712 



etc. 

If these are plotted on a uniform scale we get the result 
shown in Fig. 2A. It will be noticed that on the number 
scale the divisions grow smaller as the numbers increase. 
It is this number scale which appears on the slide rule. 
There are many subdivisions. The space from 1 to 2 is 
divided into 10 parts, and so are the other spaces. The 
space between 1 and 1.1 is also divided into ten parts; 
but above 2 there is not room for so manj^ lines, so the 
values of the divisions change and one must be on his 
guard not to make an error in scale reading. It should 
be remembered that just as the main divisions be- 
tween 1 and 10 are unequal, so are the subdivisions be- 



THE SLIDE-RULE 



37 



o 



•a 

CO 



Xi U3 

bo 

O 



o 

u 

■ O 

— |eo^ 

a 

,3 



m 



11 

CM 

o 

&0 

o 

Hi 



o 

bo 
O 



UrH i V 



T3 

© 

a 

d 
o 
o 

H 



Nf Y 



CO 



P 



C<1 

d 

1-4 



o 

d 

'■§ 
o 
p 

II 
b 



38 STATISTICAL ARITHMETIC 

tween 1 and 2 unequal. The minor subdivisions are also 
unequal but the eye cannot distinguish these small differ- 
ences. 

Let us first learn how to multiply two numbers — say 
multiply 2 by 4. We use the lower scale on the slide and 
the lower scale on the rule under it. The two scales are 
just alike. If the left-hand end of the slide is set on 2 of 
the rule, then the distance (a) along the slide is the log of 2, 
and the distance (6) along the slide is the log of 4. The 
sum of (a) and (h), i.e., (c) is the sum of the logs of 2 and 4 
and therefore is the log of their product. And so we find 
that the distance (c) from the end of the rule gives us 8, the 
result, under the figure 4 of the slide. 

Suppose, however, that we want to multiply 2 by 6. The 
distance (c) would then "Extend to 6 on the slide, or beyond 
the scale of the rule. That is the product is more than 10. 
Remembering that the log numbers repeat themselves above 
10, all we have to do is to set the right-hand instead of the 
left-hand end of the slide on the figure 2, of the rule and 
then read on the rule__the number under 6 of the slide. It is 12. 

The process of division is just the reverse of that of mul- 
tiplication. To divide 8 by 4, set 4 of the slide over 8 of 
the rule and read 1 (the end) of the slide on the rule {i.e., 2). 

The upper marks on the ordinary slide and rule are not 
needed for simple multiplication and division. The 
movable wire is used as a guide and reference mark. 

To return to our death-rate problem (above) we may 
divide 549 by 34.69 by setting 3469 on the slide over 549 of 
the rule and reading 1 of the slide on the lower scale of the 
rule. The result is 158+ as before. It is difficult to set 
3469 exactly, so it is impossible to read the result to more 
than three significant figures. 

The slide-rule does not give us the decimal points. That 
had best be determined by inspection. (There are indeed 



CLASSES, GROUPS, SERIES AND ARRAYS 39 

rules for the decimal point, but they are hard to remember 
and one should not attempt to do so.) Inspection shows 
that 34 goes in 549 more than 10 and less than 20 times; 
consequently the slide-rule result is 15.8 + . 

Slide-rules are made in many different lengths, from three 
or four inches up to twenty inches. A ten-inch rule is best 
for general use. The twenty-inch rule is easier on the eyes 
and can be read closer, but it cannot be carried in the pocket. 
Celluloid rules are the best, as the marks are clear, but 
cheap wooden rules are satisfactory for some purposes. 

Books of instruction accompany most of the high-grade 
rules anil can always be purchased. 

Every statistician ought to know how to use logarithms 
and how to read a slide-rule. Life is too short and time 
nowadays is too precious to depend upon the old methods of 
long division and multiplication if much work is to be done. 

Classification and generalization. — For purposes of 
study it is usually necessary to sort out the various data, 
divide them up into classes, groups or series and to make 
generalizations in various ways. Some of these piocesses 
are very simple; others are rather complicated. The 
methods used vary according to the nature of the problem 
at hand. As far as possible the simple methods should be 
preferred to the more complex procedures. 

Classes, groups, series and arrays. — Collections of units 
which differ from other collections by characteristics which 
cannot be expressed in figures are properly termed sections 
or classes. Thus, populations are divided into classes ac- 
cording to sex, nationality, conjugal condition, civil divisions. 

Collections of units which differ from other collections by 
characteristics which can be expressed in figures are called 
groups.^ As an example populations are divided into age 

^ This distinction is not universally made, but if rigidly adhered to 
it would result in greater clearness of expression. 



40 STATISTICAL ARITHMETIC 

groups, or into groups of persons having different weights or 
heights. 

Data are also arranged in series according to some natural 
sequence or some order of magnitude or chronological order. 
When all of the items of a given group are arranged in order 
of magnitude from small to large, or large to small, they are 
said to be placed in array. Companies of soldiers arranged 
with the tallest man at one end of a rank and grading down 
to the smallest man at the other end form an array. 

Classes of data. — Little need be said about classification 
except that the definitions of classes should be clearly and 
accurately stated, and so drawn as to be mutually exclusive, 
that is, it should not be possible for an item to appear in 
more than one class. 

Generalization of classes and groups. — The average, 
although a convenient device for generalizing the facts in a 
class or in a group of observations, has a number of short- 
comings. It does not give a true picture of the different 
items. Two groups may have the same average and yet 
be composed of very different items. Thus: 



6 


1 


6 


1 


7 


2 


7 


3 


9 
35 


28 
35 


7 


• 7 



Sum 
Average 

In a large number of items there may be one important 
item of large magnitude which might be concealed by the 
average. On the other hand a large item, if erroneous, 
might unduly raise the average and give a false generali- 
zation. Another name for the average is the mean. 

Some other forms of generalization, therefore, are neces- 
sary in statistical work. 



THE ARRAY AND ITS ANALYSIS 



41 



The array and its analysis. — If the items are arranged in 
order of magnitude with the smallest at one end and the 
largest at the other they are said to be in array. If the 
number of items is not too great this gives an excellent 
picture of the group. Thus Fig. 3 shows at a glance that 
the two groups on page 40 are different from each other. 



10 




Averagre -7 




Fig. 3. — Example of Differing Groups which have the Same Average. 



In an array the magnitude of the middle item is called the 
median. This is a very important unit in statistical analy- 
sis. The means are the same for the above-mentioned 
groups, i.e., 7, but the medians are different, i.e., 7 and 
2. The median may be the same as the mean, — in fact, 
it usually is near the mean, — ^but it need not be the same. 

The mode is the magnitude of the item which is most 
common among the items. A modish bonnet is one very 
commonly seen; it is the fashionable one. In one of our 
two groups there are two sixes and two sevens and we 



42 



STATISTICAL ARITHMETIC 



cannot tell which is the mode. They are tied for first place. 
In the other group the mode is clearly one. 

The magnitude of the item halfway between the median 
and the upper limit is called the upper quartile, and the 
corresponding item towards the lower end, the lower 
quartile. A quartile is one-quarter of the way from one 
end of the array to the other. See Fig. 4. 



15 

J 
I 


1 




Mean. =7.28 




















CH 
O 
® 

OQ 5 




1 













































































Uk2 



II 






3 

a 



Fig. 4. — An Array of Observations. 

The magnitude of the item one-tenth of the way from 
the lower to the upper limit of the array is the lower decen- 
tile. And so there may be quintiles, and other " iles." 

These various units help very much to give one a picture 
of an array. They are used in various combinations, and 
ratios are made up by using them. 

The average, together with the maximum and minimum, 
offers a common form of generalization. The median, 



GROUPS 43 

together with the upper and lower decentiles, is sometimes 
used. The quartile difference, that is the difference be- 
tween the two quartiles, is used. 

Again the ratio of the maximum (or minimum) to the 
mean, the ratio of the quartiles to the median, the ratio of 
the mean to the median, and other ratios have been used. 

Still another way is to find the extent to which the differ- 
ent items differ from the mean and study these differences. 

This subject, which involves such matters as variation, 
dispersion and the hke, takes us into the very heart of the 
statistical method and will be treated at length in Chapter 
XII. 

Groups. — The problem of arranging statistical data 
into groups is a troublesome one, — troublesome because 
there are several ways in which groups can be made and 
defined. 

Let us take the case of nine persons whose illness from 
a certain disease lasted respectively 13, 11, 6, 9, 12, 10, 8, 17 
and 13 days. We will consider these merely as whole 
numbers and try to arrange them in groups. A common 
way would be: 

(1) (2) (3) (4) 

Days 0-5 5-10 10-15 15-20 

Number of persons 4 (or 3?) 4 (or 5?) 1 

There is confusion here because one does not know 
whether to put the item 10 into the second or third group. 
The groups are not clearly stated. They are not mutually 
exclusive. 

Another way would be to arrange the groups thus, making 
the upper and lower limits both inclusive. 

(1) (2) (3) (4) (5) 

Days 1-5 6-10 11-15 16-20 

Number 4 4 1. 



44 STATISTICAL ARITHMETIC 

A better way would be this : 



Days . . . 
Number . 



(1) 


(2) 


(3) 


(4) 


0-4 


5-9 


10-14 


15-19 





3 


5 


1 



The last two methods are both used. The means for the 
four groups in the last method would be respectively 2 
(average of to 4), 7, 12 and 17. The means for the five 
groups in the next to the last method would be 0, 3, 8, 13 
and 18. 

Let us next take a case where we have to deal with whole 
numbers and fractions, — say to the nearest quarter, — 
and where the items are 54, 52 J, 51 J, 57, 50i, 54|, 51 J, 
56i, 58 inches. We may group them thus : 

(1) (2) (3) 

, ( 50, 50i 51, 5U, 52, 52i, 

\ 501, 50f 511, 51f 521, 52f 

Group limits, inches 50-50f 51-51f 52-52| 

Mean of group 50| 51| 52| 

and so on 

With measurements of quarters it is not possible to de- 
vise a grouping such that the mean of each group is an 
even number. Neither 50|-51 J nor 50j-51i would give 51 
as the mean. 

If, however, we had observations in which the fractions 
were thirds, or fifths, or with some other odd-numbered 
denominator, we might do so. Thus if we had 50f-51 J the 
mean would be 51; or if we had 50f-51f the mean would 
be 51. Sometimes it is an advantage to arrange the group 
so that the mean of the group is a whole number, but often 
this does not matter. 

Again let us suppose we are dealing with whole numbers 
and decimals (to tenths only). Here the denominator is not 
an odd number. We might arrange the groups thus : 



GROUP DESIGNATIONS 45 

(1) (2) (3) (4) 

Limits 0.1-1.0 1.1-2.0 2.1-3.0 etc. 

Mean of group 0.55 1.55* 2.55 

or 

(1) (2) (3) 

Limits 0-0.9 1.0-1.9 2.0-2.9 

Mean of group 0.45 1.45 2.45 

If the observations were made to the nearest hundredth 
we might have 

(1) (2) (3) (4) 

Limits 0.01-1.00 1.01-2.00 2.01-3.00 etc. 

Mean 0.505 1.505 2.505 

If we had observations of much greater accuracy we would 
approach the following round numbers as the means of the 
groups : 

(1) (2) (3) (4) 

Limits.. 0. + ...1.0 1.+ ..-2.0 2. + . . . 3.0 
Mean... 0.5 1.5 2.5 

Group designations. — In describing groups it is techni- 
cally proper to designate the upper and lower hmits of the 
group. For whole numbers this is perfectly simple. Thus 
in our table we may give 

Age 

(1) 0-4 

(2) 5-9 

(3) 10-14 

(4) 15-19 etc. 

If the whole numbers are followed by fractions we may 
assume that any fractions are attached to the whole num- 
bers and that the maximum figure includes the largest 
possible fraction less than one. Thus 19| would go in the 
fourth group, 14.641 would go in the third group. The 
sign (-) here stands for " to," i.e., to 4. 



46 STATISTICAL ARITHMETIC 

Sometimes to save space in printing only one group limit 
is given, the other being understood. Thus in the report 
of the Registrar General of England we find the following 
age groups tabulated : 

Age 

0- Meaning to 4 plus fractions 

5- Meaning 5 to 9 plus fractions 

10- etc. 

15- 

Where the groups differ by one, this method is the only 
practicable one. Thus 

Age 
0- 
1- 
2- 
3- 

Here we could not state an upper limit without using 
fractions. 

A better nomenclature perhaps would be to use the plus 
sign instead of the dash, indicating that any fractions were 
attached to the whole number. Thus: 

Age 
0+ 
■ 1+ 
2+ 
3+ 
etc. 

Let us compare two groupings, a and 6, the limits of 
which are stated as follows: 



a 


h 


4+ 


4-4f 


5+ 


5-5| 


6+ 


6-6| 



PERCENTAGE GROUPING 



47 



The inference would be that the first' group of a included 
items of magnitude 4 and of 4 plus any fraction attached 
to it however small. The average of the items in this 
group would be 4.5. In the case of b, however, the infer- 
ence would be that the measurements were made to the 
nearest J, and that the items in the first group would be' 
only 4, 4J, 4J or 4f , the average of which would be 4f . 

Percentage grouping. — It often happens that what is 
wanted is not so much the number of items which fall in 
each group as the relative number in the different groups. 
In this case we take the total number of items as 100 per 
cent and find the per cent which the number of items in 
each group is of the total, that is, we make a percentage 
grouping, or a percentage distribution. 

In a certain outbreak of typhoid fever the cases were 
distributed according to age as follows: 



TABLE 10 

AGE DISTRIBUTION OF TYPHOID 
FEVER CASES 



Age group. 


Number of 
cases in group. 


Per cent of 
cases in group. 


(1) 


(2) 


(3) 


Q-4 

5-9 
10-14 
15-24 
25-34 
35-44 
45- 

Total 


42 

77 
82 
140 
85 • 
45 
34 


8.3 
15.3 
16.3 
27.7 
16.8 
8.9 
6.7 


505 


100.0 



The figures in the third column are computed from those 
in the second. The use of the slide-rule greatly facilitates 
such computations. The author made the above compu- 



48 



STATISTICAL ARITHMETIC 



tation of percentages with the sUde-rule in less than two 
minutes. For comparison he made the same computations 
by long division, finding that it required three times as 
long. 

Cumulative grouping. — A cumulative or summation 
'group is one which includes the data for previous groups, 
that is, all of the data from the beginning of the series up to 
the group limit. An illustration will make this clear. 



TABLE 11 

AGE DISTRIBUTION OF CASES OF POLIOMYELITIS 
Brooklyn, N. Y., 1916 





Per cent of 


Age group 


Per cent in 


Age. 


Per cent less 


Age group. 


cases in group. 


(cumulative). 


group. 


than stated age. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


0- 


8.5 


0- 


8.5 


1 


8.5 


1- 


22.0 


0-1 


30.5 


2 


30.5 


2- 


23.9 


0-2 


54.4 


3 


54.4 


3- 


19.0 


0-3 


73.4 


4 


73.4 


4- 


7.2 


0-4 


80.6 


5 


80.6 


5- 


6.6 


0-5 


87.2 


6 


87.2 


6- 


3.7 


0-6 


90.9 


7 


90.9 


7- 


2.5 


0-7 


93.4 


8 


93.4 


8- 


1.5 


0-8 


94.9 


9 


94.9 


9- 


1.3 


0-9 


96.2 


10 


96.2 


10- 


0.8 


0-10 


97.0 


11 


97.0 


11-15 


2.0 


0-15 


99.0 


16 


99.0 


16- 


1.0 


0- 


100.0 




100.0 




100.0 





The figures in the fourtH column were obtained by suc- 
cessive additions of the figures in the second column. It is 
more common perhaps to state the results of cumulative 
grouping in the manner shown in columns five and six. 
If there are 30.5 per cent in the cumulative group 0-1, it is 
obvious that 30.5 per cent of the cases were younger than 
2 years. 



' AVERAGES 49 

The summation table is very useful in many statistical 
problems. 

Averages. — The simplest, most common, and in general 
the most useful method of generalizing the results of a set 
of observations is the average, qt arithmetic mean. The 
word mean is practically synonymous with the word average, 
but some writers apply the former to the generalization of 
a group, using the latter to indicate the arithmetical process. 

The average is found by dividing the sum of the magni- 
tudes of a* number of items by the number of items. The 

average of 13, 19 and 25 is ^^ + ^^ + ^^ = ^ = 19. The 

f io ,A in n lo- 12 + 14 + 10 + 5 + 9 50 
average of 12, 14, 10, 5 and 9 is = -^ 

= 10. 

Now what is the average of all the items in both of these 

groups? Without thinking we might say that it is ^ 

= 14. 1, but this would be wrong. To prove it add together 
the items and we have 

13 + 19 + 25 + 12 + 14 + 10 + 5 + 9 107 ,,3 



8 8 



= 131, 



which is the true answer. The reason why we cannot take 
the average of the two averages is because the second 
group has five items and the first group only three. The 
second group being larger ought to be given a greater 
weight in combining the two. 

Suppose that we give the second group greater weight 
than the first in proportion to the relative numbers of items 
in the two groups. We then have 

19 (the average of the first group) X 3 = 57 

10 (the average of the second group) X_5 = _50 

The sum is ~ 107 
and 107 -^ 8 = 13f . 



50 



STATISTICAL ARITHMETIC 



This is what is called a '' weighted aver age J' It is often 
very useful. Let us take another example of this. 

If one man in a factory earned $30 per week, three 
earned $20 and one hundred earned $10, what is the average 

30 + 20 + 10 



wage per man? Certainly not 



It is 



X 1 =i 
X 3 = 
$10 X 100 = 

104 $)1090 



i 30 

60 

1000 



110.48 

In reality this is merely an abridgment of the labor re- 
quired to add together the wages of each particular workman. 

Sometimes it is required to find the average of a series of 
observations arranged by groups. Let us assume that in 
the following table the observations are made ojily to the 
first decimal place. 

TABLE 12 



Group. 


Number in group. 


Average of group. 


Product of (2) and (3) 


(1) 


(2) 


(3) 




0-0.9 
1.0-1.9 
2.0-2.9 
3.0-3.9 


21 
17 
12 

8 
58 


0.45 
1.45 
2.45 
3.45 


9.45 
24.25 
29.40 
27.60 

58)90.70 

1.56 = 
average 



The geometric mean of two numbers is the square root of 
their product. If we have two numbers a and h, the geo- 
metric mean is Vah. It is also called the mean proportional 
between two numbers, because if we let it be represented by 
X, then a : X = X : h, i.e., a is to a; as ic is to h. By al- 
gebra, from this equation ah = x^. .^ x = 'Vah. 



AVERAGES 



/ 51 




52 



STATISTICAL ARITHMETIC 



If there are three numbers the geometric mean would be 
the cube root of the product of the three numbers; and so 
for larger numbers. 

As compared with the arithmetic mean the geometric 
mean minimizes the effect of very large numbers and 
increases the effect of very small numbers on the final re- 
sults. For instance, the arithmetic 

4 + 20 ^24 
2 ~ 2 




mean of 4 and 20 is 



= 12. The geometric mean would 
be V4X20 = VSO = 8.95. The 
arithmetic mean of 1\ and 100 
would be 51, the geometric mean 
14.1. 

Economists often use the geo- 
nietric mean in combining the 
prices of different commodities 
to obtain an index of trade con- 
ditions. It has not been much 
used in demography, but there 
are places where it might well be 
used. 

There is another kind of average 
known as the harmonic mean. A 
man travels two miles, the first at a 
rate of 10 miles per hour, the sec- 
ond at a rate of 20 miles per hour, 
what was his average rate of travel? The obvious answer, 
i.e., 15 miles per hour, is not correct, for the man did not 
travel for two hours but for two miles. Actually he 
traveled the first mile in t'o of ^^ hour, or 6 minutes, and 
the second in gV oi an hour, or 3 minutes. His average 

time, therefore, was — ^ — = ^ = 4.5 minutes per mile, and 



Fig. 6. — Machine for 
Sorting Cards. 



MECHANICAL DEVICES FOR STATISTICAL WORK 53 

his average rate ^-^ = 13.3 miles per hoiir. The statis- 
4.5 

tician seldom has occasion to use this. Algebraically the 

harmonic mean of two numbers, a and h, is — —y- 

a + t> 

In the study of data arranged in series, the items of which 
fluctuate up and down but which nevertheless show cyclical 
variations, the moving average is often computed in order to 
obtain a series from which the local fluctuations have dis- 
appeared. The moving average is a series of averages, each 
based on the same number of items, but each group of items, 
as it advances, adding one new item and dropping one old 
one. If for example we have items in this order : — 16, 14, 
18, 17, 18, 17, 19, 15, 13, 14, 11, 12, 10, 11, 8, the moving 
average based on successive groups of three items would be 
16 + 14 + 18 _ 14 + 18 + 17 _„ 18 + 17+18 
3 = ^^' 3 = ^^-^^ 3 = 

17.7; 5 = 17.3; and so on. Sometimes groups 

of five items are taken, or nine, or twenty-one, but usually 
some odd number. An example of the moving average may 
be seen in Fig. 44. Some one has said that the moving 
average is so named because the large amount of work re- 
quired moves one to tears. Any one thus affected should 
know that there are shortcuts to the results which may be 
found described in works on general statistics. The moving 
median might be used if the groups chosen contained many 
items. This would require somewhat less work than the 
moving average. 

Mechanical devices for statistical work. — It would not 
do to close this chapter on statistical arithmetic without 
calling attention to the mechanical devices now available 
for performing the operations of addition, subtraction, mul- 
tiplication and division. Where statistical operations are 



54 



STATISTICAL ARITHMETIC 



constantly going on these instruments more than pay for 
their cost. They are too well known to need description here. 
The tabulating devices of the Hollerith and Powers 
types are not as well known, but they have become an 
established feature in the U. S. Bureau of the Census and 
in the statistical departments of large commercial and 
industrial corporations. Three separate devices are re- 
quired for this work — a card punching machine, a sort- 
ing machine and a counting machine. In keeping records 




Pig. 7. — Machine for Sorting Cards. 

of deaths, the data from each death certificate are trans- 
ferred to a card, each fact being indicated by number, a 
hole being punched in the proper column. These holes 
serve as the basis of sorting in the second machine. By 
feeding the cards into the sorting machine they can be 
quickly divided into piles according to age, or sex, or cause 
of death, or into other groups or classes. The third ma- 
chine counts the cards.^ 

1 Information concerning these devices may be obtained from the 
Tabulating 'Machine Co., Ill Devonshire St., Boston, Mass. The 
author is indebted to this company for figures 5, 6 and 7. 





HARVARD UNIVERSITY - 


-DEMOGRAPHY 










DEATH CARDS, MANILA 


BIRTH CARDS, SALMON 














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56 • STATISTICAL ARITHMETIC 



EXERCISES AND QUESTIONS 

1. Define the following statistical units as used by the U. S. Bureau 
of the Census. 

a. A famUy. j. A rural community. 



6. 


A birth. 


k. 


The population of a place, 


c. 


A death. 


L 


Communicable disease. 


d. 


An infant. 


m. 


Suicide. 


e. 


A dwelling house. 


n. 


Age. 


/. 


A colored person. 


0. 


A citizen. 


g- 


A farmer. 


V- 


An industrial accident. 


h. 


A cotton-mill operative. 


q- 


A sleeping room. 


i. 


An urban community. 







2. Criticize the tables in the annual reports of any health depart- 
ment (as assigned by the instructor), as to title, form, boxing, abbrevia- 
tions, etc. 

3. Discuss the tables in the reports of the U. S. Bureau of the Census. 
Should they be taken as models? 

4. Is it good form to use the following abbreviations? 

a. "No. of Days," for Number of Days. 

b. " Pop." for population. 

c. ''Av." for average. 

d. "Ty. rate" for death-rate from typhoid fever. 

e. "T. B. rate" for death-rate from tuberculosis. 

What other iU-advised abbreviations have you observed? 

5. In one ward of a city 517 births were reported, it being estimated, 
on the basis of past experience, that this figure was within 8 per cent of 
the true number; in a second ward the report was 730 births, with an 
estimated error of 20 per cent ; in a third the corresponding figures were 
910 and 25 per cent; in a fourth, 604 and 18 per cent; what was the 
probable number of births in the city? And what was the probable 
percentage error of the total number of reported births? 

6. If the death-rate in a certain city was 20 per thousand in 1910, 
if it decreased 10 per cent the next year, increased 10 per cent the year 
after, decreased 20 per cent the next year, increased 20 per cent the next 
year, what was the death-rate in 1914? 



EXERCISES AND QUESTIONS 



57 



7. Multiply the following numbers by the arithmetic process, by the 
use of logarithms and by the use of the slide rule. Note the relative 
accuracies of the result. 



a. 
b. 
c. 
d. 
e. 


17 X 215. 
95 X 847. 
2161 X 1050. 
9230 X 40,373. 
10,072X736. 


/• 
9- 
h. 

i. 
J- 


54,672 X 93,721. 
4.7 X 1573. 
0.231 X 1.29. 
0.507 X 0.062. 
432.1 X 13.41. 


5iir 


lilarly perform the following 


divisions : 


a. 
h. 
c. 
d. 
e. 


342 - 17. 
9467 - 872. 
473,561 ^ 2395. 
100,262 ^ 730. 
0.517 -- 2.43. 


g- 

h. 
i. 
3- 


20,073 -- 98. 
763.05 ^ 40.39. 
8999 -^ 1101. 
30,500 -r 10.07. 
0.03 -=- 76. 



9. Given the following items: Find the mean, the median, the mode, 
the upper quartile. 

a. 6, 7, 6, 2, 8, 4, 9, 6, 7, 2, 1, 2, 1, 9, 8, 7, 3, 6, 6. 
h. 71, 3, 2, 0, 0, 1, 9, 5, 6, 3, 0, 2, 7, 7, 0, 4, 0, 2, 8. 
c. 2, 12, 2, 14, 3, 13, 9, 16, 1, 0, 40, 90, 3, 22, 7, 15. 

10. Arrange each of the sets of figures in the last question in groups 
as follows and find the average of each set from these groups. 



(1) 


(2) 


(3) (4) 


(5) 


Group limits (inclusive) 0-4 


5-9 


10-14 15-19 


20 and above 


Number of items in group .... 




.... .... 





11. Find the arithmetic and geometric means of: 
a, 71 and 19. h. 421 and 7. c. 21, 7 and 11. 



CHAPTER III 
STATISTICAL GRAPHICS 

Use of graphic methods. — Statistics are numerical ex- 
pressions of facts. When the facts are few in number* it is 
not necessary to use figures to represent them, but as the 
number of facts becomes larger a point is reached where 
memory of individual facts must be supplemented by 
generalizing them, by letting a number stand for a class or 
a group of facts. In the same way when the numerical 
processes become complicated, when the figures become 
unwieldy or attain magnitudes beyond the ordinary range 
of familiarity, it is useful to resort to another process and 
represent the figures graphically. And even when the facts 
are few and simple their representation by diagram is often 
a distinct aid to the mind in grasping their meaning and 
fixing them in the memory. 

There are two distinct uses of graphic methods and it is 
important to keep these in mind in preparing diagrams. 
The first use is for study. The relations between different 
groups, classes and series of facts can often be understood 
better from diagrams than from tables of figures. By the 
use of cross-section paper it is possible to interpolate values 
between plotted points, to generalize the facts of a series in 
which the data are more or less irregular, to extend plotted 
curves ahead of the data, thus enabling statistics to be used 
as a basis of prediction, to compare different curves and 
thus establish correlations. Properly used graphic methods 
will greatly assist the statistician in understanding his data. 

58 



TYPES OF DIAGRAMS 59 

It is a great mistake, however, to think that all statistics 
should be reduced to diagrammatic form, and it must be 
remembered that not one person in ten is able to read a 
complicated diagram understandingly. Some regard dia- 
grams as puzzles to be worked out. To such persons dia- 
grams are of little or no practical value. 

The other use of graphic methods is for displaying the 
facts in such a way that they will attract attention, that the 
general results, regardless of details, will fix themselves in 
the memory. This use of graphic methods has greatly 
increased in recent years. We see diagrams of all kinds on 
bill-boards, in advertisements, in public health reports, 
in popular and scientific articles, even in moving pictures. 
The growing importance of the whole subject is shown 
by the recent publication of a notable book by W. C. 
Brinton^ on Graphic Methods for Presenting Facts, which 
contains several hundred different kinds of graphic repre- 
sentations — a most useful book for statisticians to study. 

Thus, on the one hand, we have the diagram forming a 
part of mathematics, and, on the other hand, we find it 
merging into the cartoon; hence we may lay down the 
general principle that graphic methods of depicting statis- 
tics must be selected according to the use to which they are 
to be put. 

Types of diagrams. — The word diagram may be used in 
a generic sense to include all of the various kinds of mathe- 
matical graphs, plots, charts, maps and pictorial illus- 
trations used by statisticians for the display or comparison 
of numerical data. These may be roughly classified as 
follows : 

1. One-scale diagrams, in which different items are 
compared with each other on the basis of a single 
magnitude scale. 

1 See list of references in Appendix. 



60 STATISTICAL GRAPHICS 

2. Two-scale diagrams, commonly known as graphs, 

in which two magnitudes are involved. One of 
these is commonly represented by a horizontal 
scale and one by a vertical scale. These graphs 
take many forms. 

3. Three-scale diagrams. It is difficult to represent 

three dimensions on a flat sheet of paper, but it is 
sometimes done by the so-called isometric method. 

4. Component-part diagrams, in which a single quantity 

is shown in sub-division. 

5. Pictorial diagrams, or pictograms, a special form of 

the one-scale diagram used for display. 

6. Statistical maps, or cartograms, a special form of the 

two-scale diagram, in which one scale is area ar- 
ranged geographically, while the other consists of 
differently colored or shaded areas. 
There are also many miscellaneous types of diagrams 
with specially devised irregular scales, logarithmic scales, 
probability scales, etc., and with one scale superposed on 
another. These are for study and not for display. 

The appeal to the eye. — Diagrams are intended as an 
appeal to the eye, and advantage is taken of the ability of 
the eye to observe quickly and with fair accuracy: 

(a) Distances, as, for example, the relative heights of 
different points above a base line or the relative 
distances of points from some other point or from 
" some axis. 
(6) Areas, as shown by comparison of similar figures, 
that is by circles, squares, rectangles or even 
irregular figures. 

(c) Volumes, as shown by comparison of similar cubes, 

cylinders, spheres and irregular figures. 

(d) Ratios, such as the relative lengths of parallel lines, 

areas or volumes similar in general shape. 



GRAPHICAL DECEPTIONS 61 

(e) Slopes, or the relative inclinations of different lines 
from a base line. 

(/) Angles, as shown by the sub-division of the 360 de- 
grees about a point. 

(g) Shades and colors, as shown by areas on pietograms 
and maps. 

Graphical deceptions. — In preparing diagrams it is well 
to bear in mind that the eye may be deceived. There may 
be graphical fallacies as w^U as statistical fallacies. Some 
of these may be illustrated by well-known optical illusions. 

In Fig. 9 the line A appears to be longer than B. In 
reality they have the same length. The shaded area D ap- 
pears to be taller than C. In reality they have the same 
height. Astigmatism is also the cause of optical illusions. 
Those whose business it is to prepare diagrams for display 
should study these optical conditions. 

But there are other and more important ways in which 
diagrams may deceive. 

In pietograms we sometimes see two objects of different 
size — say two men, one large and one small, illustrating 
the relative numbers of persons who have died from two 
diseases. If the relative numbers are as 2 is to 1, the 
figures would naturally be drawn with the heights in that 
ratio. But to the eye the larger man would appear to be 
more than twice the size of the smaller one, because the 
eye would here judge not the height alone, but the whole 
aiea of the figure This very common fallacy in which one 
dimension is used for plotting, with no reference to the 
other dimensions which automatically changes, may be 
illustrated by the two circles E and F. The diameter of 
F is only twice that of E, but the circle F seems to be much 
more than twice as large as E. This fallacy may be called 
that of plotting by line and seeing by area. 

Similarly when a polar dia.gram is made to illustrate 



62 



STATISTICAL GRAPHICS 



the seasonal distribution of some disease, the number of 
cases per 1000 persons being indicated by the distance of 
each plotted point from the center, an incorrect idea is 
obtained. In Fig. 21 the death-rate for April and May 





D 





Fig. 9. — Optical Illusions. 

was in reality only three times that for August and Sep- 
tember, but from the diagram it looks to be more than three 
times as much. The reason is that the diagram was drawn 
as a line diagram, but the eye sees the area as well as the 
lines and the area embraced by the enveloping lines increases 
as the points become farther from the center. 



ESSENTIAL FEATURES OF A DIAGRAM 63 

Other fallacies connected with the choice of scales will be 
pointed out in the consideration of that subject. 

Essential features of a diagram. — Every diagram, save 
the very simplest, should have a title; one or more scales, 
plainly indicated; a background of cross-section, or co- 
ordinate lines; the points, lines or areas representing the 
data plotted, marked for identification; and any necessary- 
notes or explanations. As a rule diagrams should be self- 
contained, that is, they should tell the facts without regard 
to the accompanying text. 

The title may be entirely outside of the frame of coor- 
dinate lines, with the idea that if the diagram is published 
the printer will set up the title in type. This simplifies 
somewhat the construction of the diagram, but if a lantern 
sHde is made it may be that the printer's type will be found 
to appear disproportionately small. If the title is placed 
within the frame of coordinate lines these lines must be dis- 
continued and not allowed to run through the letters of the 
title. On machine-ruled paper this rule cannot hold as the 
coordinate Hnes cannot be erased. It is possible to place the 
title on a piece of white paper and paste it over the cross- 
section lines. In the case of machine-ruled tracing cloth, 
the lines may be removed by the use of xylol, or gasolene, 
and a clear background obtained for the title. 

In designing the title it is not necessary to use the words 
" Diagram showing the . . . " any more than it is necessary 
to say '' Table showing the . . . ." 

The size and shape of the diagram will depend in great 
measure upon the scales chosen, but as diagrams are very 
often reproduced, even though not drawn primarily for 
publication, it is always well to prepare them as if for 
publication. 

For the purposes of a typewritten report, diagrams 
should be kept within the limits of a rectangle 7 by 9| in. 



64 STATISTICAL GRAPHICS 

The standard typewritten paper is SJ X 11 in., but there 
should be margins of 1 in. on the top and left and i in. on 
the bottom and right for. binding and trimming. The 
paper containing the diagram should be cut 8 J by 11 in. 
Larger diagrams may of course be desirable or necessary. 

For reproduction most diagrams have to be reduced 
in size. When this is done the diagram as a whole is not 
only made smaller but the letters are made smaller and 
every line made thinner. Care should be taken therefore 
that the letters and figures used are not too small and that 
the lines are not too thin. 

As a rule letters and figures should be so placed that 
they can be easily read from the bottom or the right-hand 
edge. 

The coordinate lines are used to guide the eye and to 
enable one to read from the scale with accuracy and minute- 
ness. For display purposes, however, no more coordinate 
lines should be used than are necessary, as too many are 
confusing. The coordinate lines should be lighter in weight 
than the plotted points or lines in order that the latter may 
stand out conspicuously. 

Too many plotted lines should not be used in the same 
diagram as confusion may result. If there is more than 
one plotted line each should be clearly marked. This is 
especially important if the lines cross or meet at any point. 

Often it is desirable to have the diagram include within 
its boundaries not only the graphic representation of the 
figures, but the figures themselves. 

One-scale diagrams. — ^The simplest diagram is one where 
the magnitudes of the different items are represented by 
the relative lengths of Imes or by narrow rectangles of con- 
stant width. They are easy to understand and are useful 
for many purposes. The magnitudes represented by the 
lines may be stated m figures or there may be a scale shown 



ONE-SCALE DIAGRAMS 



65 



for comparison. See Figs. 10 and 11. The lines may be 
drawn horizontally or vertically. 

An important principle in line diagrams is that all of the 
lines should start from the same base. If this is not done 
comparison is difficult. In the case of Fig. 11, which shows 
the birth-rates and death-rates for two European countries, 



200- 



100- - 











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o 




w 




w 












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s 




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o 




3 








o 




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u 




o3 




o 




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u 




a 




C 




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X 

o 

ft 



bo 



Fig. 10. — Numbers of Deaths from Five Most Important Causes. 
Cambridge, Mass., 1915. 



it is easy to compare the births, shown by the total lengths, 
and the deaths, shown by the black, because they start 
from the left-hand line, but it is difficult to compare the 
natural increase of population in the two countries, shown 
by the white, because they have no common base. If the 
natural rate of increase is important it is better to use sepa- 
rate lines for births, deaths and increase as shown in Fig. 11, 
b and c. 



66 



STATISTICAL GRAPHICS 



It is also difficult to compare two lines which, though 
they have a common base, extend in opposite directions 
from the base. This, however, is often done with a fair 
degree of satisfaction. See Fig. 42. 




ENGLAND 

Fig. 11. — Comparison of Birth-rates, Death-rates and Rates of 

Natural Increase. 

Diagrams with rectangular coordinates. — Most of the 
diagrams used to illustrate statistics are of the two-scale 
type. There is a horizontal scale with magnitudes increas- 
ing from left to right and a vertical scale with magnitudes 
increasing from bottom to top. It is customary also to 
rule in a sort of checker-board consisting of parallel ver- 
tical and horizontal lines to guide the eye in following the 
scales across the paper. To further assist the eye heavy 
lines are used for the round numbers of the scale and finer 
lines for sub-divisions. It is good practice also to always 
use for the zero line a line as heavy as the plotted line. 
Usually this would be the bottom line and the left-hand 



DIAGRAMS WITH RECTANGULAR COORDINATES 67 

line. If there be no zero, as in the case of a scale of years, 
the heavy line would not be used. In the case of percent- 
age diagrams both the zero per cent line and the hundred 
per cent line should be heavy. The numerical values for 
the sub-divisions of the scale are shown in figures, prefer- 
ably at the bottom and left side of the diagram. Sometimes 
they are placed also at the top and right. Thus the zeros of 
both scales are supposed to be at or near the lower left- 
hand corner; but circumstances may compel some different 
arrangement. 

In diagrams of this kind time, whether in years, months 
or days, is generally expressed by the horizontal scale 
and always runs from left to right. Such diagrams are 
sometimes called historigrams, sometimes merely graphs. 

The distances measured along the vertical scale are known 
to mathematicians as ordinates, the distances on the hori- 
zontal scale as abscissce. 

There are several ways of plotting with two scales. 
One way is to use the vertical scale as a measure of the 
length of certain vertical lines, each of which represents 
the magnitude of an item, and to use the horizontal scale to 
indicate the occurrence of the item. Thus in Fig. 12 we 
have a daily record of the rainfall for one month. Each 
rainfall is represented by a line of appropriate length, the 
position of the line showing when the rain occurred. This 
method is especially adapted to events which occur intermit- 
tently, and without regular gradations, that is to discrete 
series. 

The rainfall data might have been indicated by dots, or 
crosses placed at the tops of the lines, the latter being left 
out. This would be misleading, however, unless similar 
dots or crosses were placed on the zero line for the days of no 
rainfall. This would not look well, and it is never done. 

The vertical line method or ordinate plotting is sometimes 



68 



STATISTICAL GRAPHICS 



used for plotting data in series, the horizontal scale repre- 
senting time. Thus we may compare the death-rates for 
different years by a diagram such as that shown in Fig. 13 A. 
This, however, is a continuous series and may be plotted 



a- 












































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II. 


















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31 



10 15 

July, 1917 



20 



25 



Fig. 12. — Example of Plotting a Record of Rainfall. 



40 



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02468 10 12 02468 10 12 02468 10 12 
Ordinates Profile Curve 

Fig. 13. — Example of Simple Plottings. 

as a broken line, known as a profile line, which shows 
continuity. See Fig. 13 5. For most purposes this profile 
method is to be preferred to the vertical line method, but 
the latter is perhaps understood better by persons not 
familiar with graphic methods. 



USE OF THE HORIZONTAL SCALE 



69 



Still another way would be to plot the data as dots, or 
crosses, and draw a smooth curve through them to show the 
trend of events. This implies that the data are subject 
to errors and that the smooth curve gives a better picture 
of the true events. See Fig. 13 C. The art of smoothing 
curves is described in most books on statistical technique. 
In general it may be said that^the rules usually laid down 
are based on the laws of probability. 

Use of the horizontal scale. — In the illustrations just 
given the divisions of the horizontal scale were taken to be 
definite points of time, namely days and years, each point 
being plotted directly on a vertical line. This does very 
well for plotting yearly records which run on continuously, 
and there is no objection to the method for practical pur- 
poses. It is not, however, strictly accurate, for a year is 
not a point of time, but an interval of time. It is the space 
between the lines, which represents the year, the vertical 
lines marking the boundaries. Graphs are sometimes made 
on this basis. : 

Let us plot the following numbers of deaths which oc- 
curred in the different months of a single year. • 



TABLE 13 
NUMBER OF DEATHS: EXAMPLE FOR PLOTTING 



Month. 


Deaths. 


Month. 


Deaths. 


Month. 


Deaths. 


Month. 


Deaths. 


(1) 


(2) 


(1) 


(2) 


(1) 


(2) 


(1) 


(2) 


Jan. 


40 


Apr. 


27 


July 


20 


Oct. 


17 


Feb. 


30 


May 


23 


Aug. 


17 


Nov. 


20 


Mar. 


25 


June 


25 


Sept. 


15 


Dec. 


25 



Here the problem is to divide the horizontal scale, which 
represents a year, into twelve parts, each of which represents 
a month, and plot one point for each month. Now we get 



70 



STATISTICAL GRAPHICS 



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Fig. 14. — Examples of Time Plotting. 

into trouble if we plot the data on the lines, for we might do 
this in two ways, as in Fig. 14, A and B. In one case we 
plot the point at the beginning of the month, in the other, 
at the end of the month. Of the two the latter is to be 
preferred. It would be more logical to let each month be 
represented by the space between the lines and to plot 
the points in the middle of the spaces as in Fig. 14, C or D. 
If the figures plotted represent the monthly averages of 



PLOTTING "FIGURES BY GROUPS 



71 



several items occurring in each month the method of plot- 
ting shown in Fig. 14 JS' is a proper one. Fig. 14 F shows 
how one may plot the mean as well as the maximum and 
minimum item for each month. At present there is no 
well-established custom in regard to these methods. Plot- 
ting °on the line is usually followed simply because it is 
easier and makes a neater diagram. Its illogical character 
seldom causes serious misunderstandings. 

Plotting figures by groups. — The plotting of individual 
observations is comparatively easy; but it is difficult to 
decide how to plot the totals and means of groups, and still 
more difficult if the groups are irregular. This can best be 
appreciated by an example. Let us undertake to plot the 
following data: 

TABLE 14 
DATA TO BE PLOTTED 



Age 
(last birthday). 


Number of 
cases. 


Age group. 


Number of 
cases in 
group. 


Average number 

of cases for each 

year. 


(1) 


(2) 


(3) 


(4) 


(5) 





1 










1 


• 2 










2 


2 




0-4 


12 


2.4 


3 


4 










4 


3 










6 


1 










6 


4 










7 


3 




5-9 


15 


3.0 


8 


5 










9 


2 










10 


6 










11 


4 










12 


7 




10-14 


25 


5.0 


13 


5 










14 


3 










15 


4 










16 


6 










17 


5 




15-19 


20 


4.0 


18 


3 










19 


2 











72 



STATISTICAL GRAPHICS 



If we plot the individual items we have the result shown 
in Fig. 15 A. If we plot the total numbers of cases in 
each group we may do so by the methods B, C, or D. 
In these the horizontal scale represents not individual ages, 
but groups. We may indicate this fact by using the 
hyphens as shown. In B we have plotted the figure 12 on 
the line which indicates the maximum limit of the group 
0-4, 15 on the line which indicates the maximum limit of 
group" 5-9, etc. In C we have plotted 12, 15, etc., in the 
middle of the spaces which represent the groups. In D 
the height of the horizontal line above the base is taken 
to represent the total and extends across the group limits. 
If we wish to show both the individual observations and 
the means for the groups we may plot as in E. 

In plotting by groups care should be taken to make it 
clear that the horizontal scale stands for groups and that 
the vertical scale stands for the number in the group. 

Plotting irregular groups. — Let us now take the case 
of irregular groupings. Assume the following data: 



TABLE 15 
DATA TO BE PLOTTED 



Age group. 


Number of 
cases in group. 


Average for 

each year in 

group. 


(1) 


(2) 


(3) 


' 0- 4 

5- 9 
10-14 
15-19 
20-29 
30-39 
40-59 
60-79 
80-99 


4 
6 
8 
6 
7 
5 
8 
6 
3 


0^8 

1.2 ' 

1.6 

1.2 

0.7 

0.5 

0.4 

0.3 

0.15 



PLOTTING IRREGULAR GROUPS 



73 









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Age Group 




Age Group 



Age Grgup 



1 1 — ■ f ■ ^ 
C 

— _^> — >^'^:^ — 

r ' — • '■ 

— ' ! 

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5 10 15 20 

Age Group 

Fig. 15. — Examples of Age Plotting. 



74 



STATISTICAL GRAPHICS 















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2 ko o 



SUMMATION DIAGRAMS 75 

In the first place we must find some way to indicate to 
the eye the varying intervals of the group. The first four 
groups cover five years, the next two ten years and the 
last three twenty years each. We might do this as in 
Fig. 16 A, in which the heavy vertical lines indicate the 
group limits. In B the coordinate lines are regular and the 
group limits are shown by the emphasized horizontal scale. 
In C the blocks indicate the group limits. Not one of these, 
however, gives an adequate picture of the distribution of 
the cases according to age, because the groups are not 
uniform. All three diagrams are fallacious because the 
ordinates are not strictly comparable. The best way to 
show distribution by age is to make the groups comparable 
by reducing all to a common denominator. This can be 
done by finding the average number of cases for each year 
in the group. The results are shown in Fig. 16 D. Here 
the irregular grouping on the horizontal scale is maintained, 
yet a good idea is given of the distribution of the cases 
according to age. 

Summation diagrams. — For many purposes it is desir- 
able to plot the results obtained by the successive summa- 
tion of the items in preceding groups. This gives what are 
called summation diagrams, cumulative plots, mass plots or 
mass curves. This may be illustrated by the data on p. 77. 

These data are plotted in Fig. 17. Sometimes instead 
of connecting the plotted points by straight lines a curved 
line passing approximately through them is sketched in. 
It should be noticed that in this diagram the horizontal 
scale stands for age and not for age-groups. 

One use which can be made of a plot of this kind is to 
find the median of the series. There are 53 cases in all. 
The middle one is the 27th. From the scale this item has a 
value of 24 j^ears, as shown by the cross. In the same way 
the quar tiles may be found and the decentiles. 



76 



STATISTICAL GRAPHICS 



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50 


































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B 










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20 








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/ 










































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10 aO 30 40 50 60 70 80 90 , 100 

Age 

Fig. 17. — Example of Cumulative, or Summation Plotting. 



CHOICE OF SCALES 



77 



TABLE 16 
DATA TO BE PLOTTED 



Age-group. 


Number of 
cases. 


Summation group. 


Number of 
cases. 


Less than age. 


(1) 


(2) 


(3) 


^4) 


(5) 


0-4 

5-9 
10-14 
15-19 
20-29 
30-39 
40-59 
60-79 
80-99 
Total 


4 
6 
8 
6 
7 
5 
8 
6 
3 
53 


0-4 

0-9 

0-14 

0-19 

0-29 

0-39 

0-59 

0-79 

0-99 


4 
10 
18 
24 
31 
36 
44 
50 
53 

53 


5 
10 
15 
20 
30 
40 
60 
80 
100 



Another use is that of redistributing the cases according 
to a different age-grouping. Let us suppose that we desire 
to find the number of cases between the ages of 35 and 45, 
i.e., in age-group 35-44. From the vertical scale and the 
plotted curve we find that there are 38 cases below age 45 
and 33 cases (approximately) below age 35, hence there 
are 38 — 33 = 5 cases in age-group 35-44. This principle 
may be usefully applied in redistributing the population of 
a city into age-groups in connection with the computation 
of specific death-rates. 

Choice of scales. — The choice of both scales is a matter 
of great importance, for it not only influences the size and 
shape of the diagram, but controls the slopes of plotted lines 
and the apparent differences between plotted points. In 
Fig. 18 we have the death-rates of Moscow from 1881 to 
1910 plotted by five-year groups according to two dif- 
ferent scales. The two diagrams look to be quite different, 
and B gives the impression of a greater decrease in rate 



78 



STATISTICAL GRAPHICS 



oSO 




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— 


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i^ 




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— 








— 


^^ 


^^ 


— 
















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h' 














































































than A because on account of the greater vertical scale 
and the smaller horizontal scale the slope of the plotted 
line is more. 

Sometimes for purposes of comparison two lines are 
plotted on the same sheet, each having its own vertical 

scale. Here the choice of 
the proper scale 'is all-im- 
portant. 

It sometimes happens 

that in order to show the 

desired variations in a series 

i i i I i i i of plotted ordinates a scale 

must be chosen so large 
that the zero point would 
fall too far below the 
plotted point to have it ap- 
pear on the diagram. Right 
here lurks a graphical fallacy 
which may be serious. It is 
best appreciated by study- 
ing an actual illustration. 

Fig. 19 shows the general 
death-rate and the tuber- 
culosis death-rate per 1000 
inhabitants in Boston, 
Moscow, Massachusetts, from 1881 
to 1911, the figures being 
plotted in five-year groups. 
In A different scales are used and the scales do not ex- 
tend to zero, on the base line. In B the same scale is 
used for both series of items. From diagram A one would 
get the idea that the tuberculosis rate was decreasing 
much faster than the general death-rate, but from diagram 
B the opposite idea would be obtained. 



35 



25 



-20 

«^ 15 

10 



_ 


— 




n 






















-^ 


^ 





— 












































B 



























































































o lO Q irj Q ira o 

OO 00 Ci 05 O O tH 

00 CO 00 00 o» OS OS 

r-» i-( T-H r-( T-t rH r-t 



Fig. 18. — Death-rates 

1881-1910. Showing Effect of 
Changing Scales. 



CHOICE OF SCALES 



79 



















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Fig, 19. — Comparison of Deaths from Tuberculosis with Deaths 
from all Causes: Boston, Mass. A, Incorrect Method. B, 
Correct Method. 



80 



STATISTICAL GRAPHICS 



100 



90 



S 80 



70 



60 



50 



40 



80, 



100 



90 



80 



70 



60 



50 



40 



30 



20 



10 



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90 
80 
70 
60 
50 
40 
30. 


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Fig. 20. — Example of Not Carrying Scale to Base Line, 
culosis Death-rate: Boston, Mass. 



Tuber- 



DOUBLE COORDINATE PAPER SI 

Fig. 20 shows the reduction of the tuberculosis death- 
rate in Boston expressed in terms of the percentage which 
the death-rate of each period was of that for the period 1881 
to 1885. In B the vertical scale is carried down to per 
cent at the base line. This gives a true picture of the re- 
duction which has taken place and the death-rate remaining. 
In A the vertical scale is not carried to the base line and the 
diagram gives the optical impression that the reduction 
has been greater than it actually has been and that the rate 
at the end of the period was very much less than at the 
beginning. Brinton has suggested that when the base line 
does not represent the zero of the vertical scale it should be 
drawn as a wavy line instead of a straight line, and this 
idea has much merit. Where two different vertical scales 
are used, and one goes to zero at the base line while the other 
does not, the wavy line may extend only half way across 
the diagram from that side of the diagram where the scale 
does not go to zero. C in Fig. 20 illustrates the appear- 
ance of a diagram drawn in this way. The wavy line 
implies that the lower part of the diagram is omitted. 

Diagrams with polar coordinates. — Fig. 21 illustrates 
a diagram with the ordinates represented by distances 
from a central point along radial lines, the abscissae, if we 
may use the term out of its place, being represented by the 
angle which the ordinate makes with the vertical measured 
clockwise around the circle. This form of plotting has 
a limited application and because of its inherent fallacious 
character should be abandoned. 

Double coordinate paper. — Sometimes it is convenient 
to use what may be called double coordinate paper. This 
is illustrated by Fig. 22. Here the plotted line may be 
read against either set of coordinates. The horizontal 
lines give the number of deaths from typhoid fever, the 
scale being at the left. The inclined lines give the death- 



82 



STATISTICAL GRAPHICS 



rate per 100,000. Thus in 1900 the number of deaths 
was about 305, the death-rate about 27 per 100,000. The 
slope of the inchned Hues depends upon the increase in 
population. The black inclined line represents popula- 
tion and this may be read for the censal years from the 
right-hand scale. It will be seen that the ratio between 



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w 


A/yVy/^A/yli '^' r"T T~ir 


W- 






m 


^-^ 


\ 


V 


t-s 




y 



Fig. 21. — Example of Radial Plotting. 

the right-hand and left-hand scale for any horizontal line 

gives the rate for the heavy line, ^.e., 200 -^ 1,000,000 = 

20 

, or 20 per hundred thousand. So also 100 -^ 500,000 

= 20 per hundred thousand. Any point on the heavy 
line, therefore, gives a rate of 20 per hundred thousand. 
The rate Hne for 10 per 100,000 is one-half way to the line • 
between the heavy line and the zero or base line, on each 
vertical line which represents a census. The rate line of 30 
is, on each vertical, as far above the black line as the^rate 
line of 10 is below it. And so on. 

In the example chosen the typhoid fever rate in Brooklyn 
has fallen since the date of the last plotting, z.e., 1906. 



RATIO CROSS-SECTION PAPER 



83 



Nouvmdod 



S061 



0061 



9681 



0681 



S881 



0881 



fiZ8L 



0Z81 




a 

o3 



c3 

Q 

as 



S S 

S § 

ft 

03 
CD 
U 
t-i 

O 



02 



^O 



o3 



d 

M 



ff3A3d aioHdAX MOUd SHxv^a do daaiNnN 



Ratio cross-section paper. — Thus far we have been 
deahng with regular scales in which the intervals are uni- 
form from one end to the other. It is possible to construct 
scales with intervals which are not uniform, but which vary 
in a systematic way. These are vised for special purposes. 
The most common scale of this kind is the logarithmic scale. 



84 



STATISTICAL GRAPHICS 



Diagrams in which the vertical scale is logarithmic and the 

horizontal scale uniform are sometimes called '' ratio 

charts." These have been used by engineers for many 

years, but they are only beginning to be appreciated by 

statisticians. 

r^It will be recalled that the logarithms of the decimal 

numbers are as follows: 

TABLE 17 
LOGARITHMS OF NUMBERS 



Number. 


Logarithm. 


(1) 


(2) 


1 


0.000 


10 


1.000 


100 


2. coo 


1,000 


3.000 


10,000 


4.000 


100,000 


5.000 


1,000,000 


6.000 



As each number increases tenfold the logarithm increases 
by one; and in general it may be said that as numbers 
increase at a regular rate the logarithms increase by a 
regular increment. From the logarithm tables ^ it may be 
seen that the log of 10 is 1.0000, and that if 10 is increased 
by 25 per cent and becomes 12.5 the log of 12.5 is 1.0969, 
an increment of 0.0969. The log of 50 is 1.6990. 50 in- 
creased by 25 per cent is 62.5. The log of 62.5 is 1.7959, * 
an increment of 0.0969 as before. The log of 1570 is 3.1959. 
1570 increased by 25 per cent is 1962.5 and the log of this 
is 3.2928, an increment of 0.0969 as before. If, using a 
uniform scale, we plot figures which increase at a constant 
rate we shall get a curve as shown in Fig. 23 A. Let us 

1 See Appendix. 



RATIO CROSS-SECTION PAPER 



85 



800 



^ 200 



100 



A 




^ CO 

§.2 

Hi 



800 
875 
250 
225 
200 
175 

150 
125 



100 



C 



8 S 

5> (35 



i 



Fig. 23. — Example of Logarithmic Plotting. 



86 



STATISTICAL GRAPHICS 



start with a population of 100 in 1870 and assume an in- 
crease of 20 per cent each decade. . We then have the 
following : 

TABLE 18 

DATA TO BE PLOTTED 



Year. 


Population. 


Log of popu- 
lation. 


(1) 


(2) 


(3) 


1870 
1880 
1890 
1900 
1910 
1920 
1930 


100 
120 
144 
173 

207 
248 
299 


2.0000 
2.0792 
2.1584 
2.2380 
2.3160 
2.3945 
2.4757 



The figures in column (2) are plotted in A. If we plot the 
logarithms of the numbers in column (2) we have a straight 
line as in B. This being so, why not label the horizontal 
lines with the numbers in column (2) instead of their 
logarithms? This is done at the right of the diagram. It 
will be seen that the vertical scale is not made up of uni- 
form intervals, but aside from that fact it is a perfectly 
good scale. In C we have a diagram in which the vertical 
scale (represented by the horizontal lines) is drawn on this 
basis, and it will be seen that the figures in column (2) 
plotted on it fall in a straight line. This is a single loga- 
rithmic, or in simpler words, a ratio chart. Figures increas-* 
ing at a constant rate plot out as a straight line on paper 
thus ruled, i.e., with a uniform horizontal scale and a 
logarithmic vertical scale. 

There are two uses for single logarithmic paper. One is 
to show variations in rate. If we plot the population of 
the United States on ordinary cross-section paper with 



RULED PAPER 87 

uniform scales we obtain an ascending curve, but from this 
we get no idea of the constancy of the rate of increase. 
This is shown in Fig. 24 A. But if we use ratio cross- 
section paper, as in B, we find that the rate of increase 
was constant from^ 1790 to 1860, but that since the Civil 
War the rate has been nearly constant yet not as great as 
before. On this paper equal slopes mean equal rates of in- 
crease, while on uniform paper equal slopes mean equal in- 
crements. 

Another use is that of enabling us to plot on one sheet 
observations which cover a very wide range. If we were 
using a uniform scale to plot such figures we should have to 
make the scale so small that individual differences between 
the small numbers could not be discerned. It will be 
noticed that on the ratio paper the intervals for the small 
numbers are larger than for the high numbers, so that if 
plotted on this paper we can still read differences in the 
lower part of the scale. The upper part of the scale is 
foreshortened. In fact we can discern the same percent- 
age differences in all parts of the scale. 

Logarithmic cross-section paper. — By logarithmic cross- 
section paper we usually mean paper on which both the 
horizontal and the vertical scales are logarithmic. Here 
the ratios are in both directions. It will be observed that 
the interval from 1 to 10 is the same as that from 10 to 100, 
from 100 to 1000 and so on. ' One objection to the loga- 
rithmic scale is that it does not go to zero. The interval 
below 1 runs from 1 to 0.1, the next from 0.1 to 0.01, the 
next from 0.01 to 0.001 and so on. 

This paper is very largely used in scientific work, but its 
use for statistical purposes is somewhat limited. 

Ruled paper. — It is not difficult to rule your own cross- 
section paper, although it is tedious work. Many sorts 
of ruled papers are on the market and can be purchased 



88 



STATISTICAL GRAPHICS 

























/ 
























/ 






















/ 


/ 




















/ 


/ 






















/ 






















/ 






















y 




















^ 


y" 


















^ 


---' 
















. — 










Dire 


3t Sea 


le 










A 
















































^^,,0^^ 
























"""^ 




















^^ 


-"■^""^ 












































^^^ 






















^."^ 




















^ 


y 


















^ 


^ 


.y'^ 


















y^ 


'^^ 






















^ 
























^ 












































- ^^' 
























^ 
















































































Lo 


^•aritb 


mio S< 


;ale 











^ 



^ a ?3 



B 



Fig. 24. 



Population of the United States shown by Direct and 
Logarithmic Plotting. 



MECHANICS OF DIAGRAM MAKING 89 

from dealers in engineering drawing materials. The fol- 
lowing scales are convenient for ordinary work: 

(a) Inches subdivided into tenths in both directions. 

(6) Half inches subdivided into tenths in both directions. 

(c) Inches subdivided into tenths in one direction and 

into twelfths in the other direction, — useful for 
plotting data for the twelve months of a year. 

(d) Ratio paper, with inches subdivided into tenths in 

one direction, and with a logarithmic scale from 
1 to 10,000 in the other direction. 

(e) Arithmetical probability paper. 
(/) Logarithmic probability paper. 

(g) Paper with horizontal scale ruled for the calendar 
year, and vertical scale in inches subdivided to 
tenths. 
It is possible to buy tracing cloth ruled in cross-section 
form, but the kinds of ruling are limited. Such cross- 
section tracing cloth is sold by the yard, width about 
26 in., and may be cut to sheets of desired size. 

Mechanics of diagram making. — For making diagrams 
it is advisable to provide a regular draughtsman's equip- 
ment. This should include: 

(a) A drawing board of appropriate size. For small 
diagrams a size of about 12 in. by 17 in. is satis- 
factory. 
(h) A tee-square long enough to extend across the 
drawing board. 

(c) A 30-degree triangle, 10 in. long, celluloid. 

(d) A 45-degree triangle, 6 in. long, celluloid. 

(e) A lettering triangle, to give slopes for letters. 
(/) A ruling pen. 

(g) One or more scales, steel, celluloid or boxwood, 

variously ruled in tenths, quarters, etc. 
{k) Black drawing ink (Higgins). 



90 



STATISTICAL GRAPHICS 





"■ 




























































































































































D 
















































































































































1 



Jan. 
F 



Fig. 25. — Examples of Plotting Paper. Sheets 8| X 11 inches. 



LETTERING 9l 

(i) Thumb tacks. 

(j) Brown '' detail " paper. 

(k) Tracing cloth. 

Other equipment may be needed according to the nature 
of the work. 

Lettering. — There is much truth in the statement that 
good letterers are born and not made. Yet it is surprising 
how much one can improve in lettering by giving attention 
to a few guiding principles. 

For most diagrams it is best to adopt a very simple style 
of letter. Shaded letters look well on maps, but are out of 
place on hne diagrams. The two styles shown in Fig. 26 
are suitable for ordinary work. The choice of a vertical 
letter or a sloping letter is largely a matter of taste. Most 
people are more successful with sloping letters. They can 
be made a little more rapidly, but they are perhaps a little 
more informal than vertical letters. 

It is important that letters appear to be uniform in 
height and slope. It is well to use guides both as to height 
and slope. Letters should also appear to be spaced uni- 
formly. The curves of such letters as C, G, and S should 
extend slightly above and below the horizontal guide lines. 
Adjacent straight-line letters such as N, I, U, M, etc., 
should be spaced a little farther apart than curved letters. 
Attention should be given to the manner of making the 
strokes as shown in the plate. 

The student should consult a book on lettering such, for 
example, as that of Reinhardt. 

If the title is inset it should be carefully placed. In 
general the lower right-hand corner is the best place for it, 
but often its location is governed by available space. 
The sizes of letters used should follow the important words. 
Each line should be centered. Write each line on a scrap 
of paper: count the letters in it: find the middle letter: 



92 



STATISTICAL GRAPHICS 



□) 



N 



IT 



■-•:> en 



>> 



o!i 



• .* 



n<t 



•■S 



■V. 




^ 



^:> 



3: 



N 



\ 



t 



N 



;3 



:sj 



ii W 



u 

o 
q: 

h 

(0 

o 

z 

< 






■l(^l« 



•5. 



ji~ 



iOin 






ip^ 



put that down first and then letter backwards and forwards. 
Capitals may be used for the principal lines of a title. In 
a general sort of way try to arrange the line^ so that a line 
circumscribing the title will be approximately an ellipse. 

Label each scale, except that it is unnecessary to do so 
in the case of months and years. Do not use abbreviations. 



THE USE OF COLOR IN DIAGRAMS 93 

If there is more than one plotted Hne label each one. Be 
free in the use of explanatory notes. A diagram should 
tell its own story. In doing this use letters of readable size. 
It is a good rule never to make a letter or a figure less than 
I inch in height. 

Somewhere on the sheet, but outside of the diagram 
itself, should be placed the initials of the person who made 
the diagram and the date. This is valuable for identifica- 
tion, but it need not be published. 

Wall charts. — Wall charts are much used nowadays in 
the display of vibal statistics. It is not difficult to prepare 
these, but certain general principles should be kept in 
mind. They should be simple and clear, of ample size 
and plainly lettered. If intended to be seen from a dis- 
tance the letters should be large and the lines heavy. As 
lettering forms an important part of a wall diagram it is 
well to know that gummed letters of all sizes can be pur- 
chased. Examples of these letters are shown in Fig. 27. 

The use of color in diagrams. — Colored fines should be 
used sparingly if the diagrams are to be published. A 
sheet must go through the press once for each color and this 
adds to the cost. The most effective use of color is where 
a single colored line is made to stand out in contrast to 
other black lines, and for this purpose red is the best. 
Color on plotted lines may be avoided by using black lines 
made in different ways. The following are easily dis- 
tinguishable : 



1. Heavy full line 

2. Light fuU fine 

3. Heavy broken line 

4. Light broken line 

5. Dotted line 

6. Dot-dash line 



94 ' STATISTICAL GRAPHICS 

For wall charts or posters intended to be viewed from a 
distance, colors are justifiable. 

The cross-section lines on the ruled paper ordinarily sold 
are colored green or brown or light red. Very bright colors 

1234567890. 







Fig. 27. — Examples of Gummed Letters, Useful for Wall 

Diagrams. 

used for this purpose are exceedingly trying on the eyes. 
It is desirable however to have a color which can be pho- 
tographed and also blue-printed. Green is not satisfac- 
tory from these points of view. Dull red is much better. 
Vermilion red should be used, not carmine. 



COMPONENT PART DIAGRAMS 



95 



Component part diagrams. — In order to show the com- 
ponent parts of a total number we may subdivide a hne or 
a long rectangle and label each part, or we may subdivide 
an area, as a square or a circle, indicating differences by 




Disease 



Fig. 28. — Proportion of Deaths from Each Specified Cause iu 
the U. S. Registration Area: 1907. 



colors, shades or patterns as in cartography. A circle 
properly subdivided is perhaps the best type of diagram to 
show percentages. Here the sectors plainly show the de- 
sired differences. This sort of a diagram is not to be. con- 
fused with plotting by polar coordinates. (See Fig. 28.) 



96 STATISTICAL GRAPHICS 

Statistical maps. — The object of statistical maps is to 
display classes and groups of statistics for different areas. 
It will be remembered that statistical classes involve differ- 
ences which cannot be expressed in figures, but that statisti- 
cal groups contain facts similar in kind but which differ from 
each other numerically. This difference should be kept in 
mind in preparing statistical maps. 

The statistical data are shown on maps by different 
colors, by different patterns of lines and dots or by sur- 
face shadings. In the display of data arranged in groups, 
that is, in accordance with magnitude, it is well to indicate 
the differences by variations in shade from light to dark. 
In the display of data arranged by classes it is well to use 
different patterns or colors. Different shades may be ob- 
tained by successive washes of color applied with a brush, 
or by the use of cross-hatching in which the proportion of 
surface covered with ink regularly increases. The so-called 
^' Ben Day " system of indicating shades by the use of 
special devices is well known to printers and engravers.^ 

Sometimes the figures themselves are placed on the maps. 
If this is done care should be taken to make sure that the 
boundaries of the areas to which the figures apply are prop- 
erly defined. 

Blue prints and other prints. — It is often desirable to 
obtain several copies of the diagrams made, and the quickest 
and cheapest method is that of making blue prints. The 
process is the same as that of making photographic prints 
from a negative. Blue-print paper can be purchased; in 
fact, it can be easily made. A large photographic printing 
frame is required. The diagram is placed in the frame over 
the blue-print paper and exposed to the sunlight for a 
few minutes, after which the paper is washed in water and 
dried. It is necessary, of course, to have the paper on 
, ^ See Brinton's Graphic Methods, pp. 216, 23'3. 



REPRODUCTION OF DIAGRAMS 97 

which the diagram is made fairly thin and transparent. 
Paper should be selected with blue-printing in mind. The 
transparency of paper can be greatly increased by oiling it 
on the back after the diagram is made. A liquid sold 
under the name of '' transparantine " is satisfactory. The 
best blue prints of diagrams are obtained by the use of trac- 
ing cloth. This has many advantages. It is easy to ink 
on and erasures may be made. The lines are sharp and 
photograph well. The cloth does not tear. The cloth is 
oiled on one side. The drawing should be done on the other. 
A little powdered chalk should be dusted on and rubbed off 
before using ink. Pencil lines may be used as guide lines 
and erased before blue-printing. 

In the ordinary blue print the lines are white and the 
background blue. Additional white lines can be drawn on 
the blue by using a weak solution of caustic soda in a pen 
as ink. 

It is possible to obtain prints in which blue or brown 
lines appear on a white ground. This requires the making 
of a negative, from which subsequent prints are made. 

Reproduction of diagrams. — The common method of 
reproducing diagrams for publication is to photograph them 
and print from a zinc plate. This is the cheapest and most 
available method. It is necessary that the original draw- 
ing be well made, with lines of the right weight and the 
letters of the right size. All imperfections are of course 
reproduced. Usually the drawing should be made at least 
fifty per cent larger than the published plate, that is, the size 
is reduced one-third. To have diagrams made by a 
draughtsman costs something, but, if the photographic 
process is to be used, it is worth while. The draughtsman 
should know what the size of the published plate is to be. 

Those not skilled in making diagrams ought to know that 
there is another process of reproduction which does not 



98 STATISTICAL GRAPHICS 

require a carefully drawn oiiginal, namely, that of wax 
engraving. In this process the engraver does the work of 
the draughtsman. A copper plate is used. The lettering 
in this process can be put in with type. This results in per- 
fect legibility, which is often not the case with photographic 
work. Reproduction by the wax process costs almost 
twice that by the photographic process, but if to the 
latter is added the time and expense of preparing a perfect 
original the wax process costs no more. Most of the plates 
in this book were made by the wax process by the L. L. 
Poates Company of New York. Unfortunately there are 
not many wax engravers in this country. 

Equation of a curve. — Having plotted certain data on 
rectangular coordinate paper, that is, using a horizontal 
and a vertical scale, and finding that the points fall on a 
straight line or on a regular curve, it is sometimes desirable 
to find the equation of the straight line or curve. This is 
not difficult, but it requires the use of mathematical prin- 
ciples not considered in this book. The reader is referred 
to such books as Saxelby's ^'A Course in Practical Mathe- 
matics" ^ or Peddles' '^Construction of Graphical Charts." ^ 

EXERCISES AND QUESTIONS 

1. Describe Ripley's method of preparing statistical maps with 
different shadings. [Pub. Am. Sta. Asso., Sept. 1899, pp. 319-322.] 

2. Construct a graph of the birth-rates and death-rates of Sweden 
from 1749 to 1900. (See p. 203.) 

3. Construct a graph of the natural rate of increase of the population 
of Sweden from 1749 to 1900. 

4. Show by suitable diagrams the data in Tables 100, 106 and 110. 

5. Find diagrams in this book which do not conform to the principles 
described in Chapter III. 

^ Pub. by Longmans, Green & Co., 1908. 
2 Pub. by McGraw-Hill Book Co., 1910, 



i 



EXERCISES AND QUESTIONS 99 

6. Construct a "devil's checker-board," as follows: 

a. Take a piece of cardboard or heavy drawing paper and rule in 
black ink a rectangle 8^" wide and 11" high. Rule also a horizontal 
line 1" below the top, and a vertical line 1" from left-hand edge, in order 
to leave suitable margins at top and left. 

h. . Subdivide the 7^" on the horizontal line into 15 half -inch spaces 
and rule vertical lines. Subdivide the 10" on the vertical line into 40 
quarter-inch spaces and rule horizontal lines. 

c. Draw in red inclined lines sloping downward to the left, being Y' 
apart in a horizontal line and Ij" apart in a vertical direction. 

If the work is done accurately certain of these diagonals will intersect 
corners of the small rectangles; if the work is not accurate the name of 
the problem is justified. These guide lines will be found convenient in 
the construction of tables. The sloping lines will serve as guides for 
sloping letters. 

7. Construct a colored wall chart showing the death-rates from 
several diseases for some city, using the one-scale type of diagram. 
Assiune the chart is to be read from a distance of twenty feet. 

8. Describe the method of construction and the varied uses of ratio 
cross-section paper. (Quar. Pub. Am. Sta. Asso. June, 1917, p. 577.) 

9. Plot the population of some city (assigned by the instructor) using 
ordinary cross-section paper and ratio paper. 

10. Construct a colored component-part diagram (subdivided circle), 
showing the composition of the population of some city or state (data 
assigned by the instructor) . 



CHAPTER IV 
ENUMERATION AND REGISTRATION 

All civilized nations at regular periods enumerate their 
populations, that is, take a census. There are various 
governmental reasons for doing this, two important ones 
being the adjustment of representation in legislative bodies 
and the levying of taxes. There are also business, social 
and sanitary uses to which the figures are put. In consid- 
ering a census several questions immediately arise;' when 
was it made, what area was included, how were the data 
obtained, what were the results and where may they be 
found? 

The United States census. — The first general census of 
the United States was made in 1790, the first year divisible 
by ten after the founding of the new republic, and a census 
has been taken every ten years* since that date, the census 
of 1910 being the thirteenth. 

The first twelve censuses were made by special commis- 
sions created for the purpose and which went out of exist- 
ence as soon as the task had been accomplished. A per- 
manent Bureau of the Census was created in 1902. At 
first it was under the Department of the Interior, but in 
1903 was transferred to the Department of Commerce and 
Labor. Its head is known as the Director of the Census. 
Besides taking the general census of the country every 
ten years this bureau is charged with the collection of sta- 
tistics of many kinds relating to the people, vital statistics, 
financial statistics, municipal statistics, statistics of agri- 

100 



THE UNITED STATES CENSUS 101 

culture, fishing, manufacture, transportation, mining, and 
others. 

The census data prior to 1910 were published as a series 
of special volumes by the commission having the work in 
charge. Many of the older volumes are out of print, but 
may be found in large libraries. In 1900 there were three 
volumes on population and two volumes on vital statistics 
obtainable by purchase from the U. S. Publication Office at 
Washington. Bulletins of the census of 1910 may be ob- 
tained from the ^' Director of the Census, Washington, 
D. C." Lists of available reports and bulletins may be 
obtained without charge by writing to the director. 

In 1910 the report of population comprised four large 
volumes. The first contained the general data for the coun- 
try, classified and grouped in many ways; the second and 
third gave the population subdivided by civil divisions; 
the fourth, occupations. For some time it has been cus- 
tomary to include in each census report the populations for 
the two censuses preceding. This is for comparison and to 
enable estimates of population to be made. Thus, in the 
thirteenth census will be found the populations for 1910, 
1900 and 1890. 

A table often consulted was that on page 430 of Vol. I, 
Part I, of the U. S. Census of 1900, which gave the popula- 
tions of all cities which were larger than 25,000 in 1900, for 
every census since 1790. In the 1910 census these figures are 
given in the second and third volumes mentioned under the 
head of each state. See also pages 80-97 of the first volume. 

These census reports should be in every public library, 
and in the library of every city government, as they con- 
tain a vast amount of important information relative to 
the growth and condition of our country. Every student 
of demography should become thoroughly familiar with 
the U. S. Census reports. 



102 ENUMERATION AND REGISTRATION 

The census date. — For most purposes it is sufficiently 
accurate to say that the census was taken in a certain 
year, but for the more exact computations a definite day 
must be named. The population of the country is con- 
stantly changing, even from hour to hour. If we wish to 
use the figure which best represents the population for 
any year we should naturally choose the population as it 
was at the middle of the year, namely July 1st. But it is 
not practicable to enumerate all of the people on a single 
day, and July 1st is not the best time to make the enumer- 
ation because being in the vacation season many people 
are likely to be away from home. For practical reasons 
another day is chosen as the official day for taking the 
census. 

In 1910 this day was April 15th. It took several weeks 
to make the enumeration, but the data were adjusted to 
this day so that the statistics are stated '' as of April 15th." 
But it should be noted that in 1900, in 1890, and back to 
1830 the official date was June 1. Hence between the 
census of 1900 and 1910 the interval was not 10 years, but 
ten years less 1| months (April 15 to June 1) or IJ per cent 
less than ten years. In some computations this introduces 
an appreciable error and a correction must be made. From 
1820 back to 1790 the day of the census was the first Mon- 
day in August. 

In Great Britain, including Canada and Australia, the 
national census is taken every ten years, but one year later 
than in the United States, that is, in 1901 and 1911. This 
has been so since 1801. The time of the census is '' at mid- 
night before the first Monday in April." 

It is quite possible to adjust the population of the census 
year, 1910, so as to find what it was on July 1st of that year, 
and this has been done by the IT. S. Census Bureau and the 
figures used for the computation of mortality statistics for 



THE ENUMERATION SCHEDULE OF 1910 103 

that year. The method used is described in the next 
chapter. 

- Civil divisions. — The population of the United States is 
given in the census reports by minor civil divisions. The 
total population of the nation is subdivided into continen- 
tal and ^' non-contiguous territory/' the latter including 
Alaska, the Hawaiian Islands, Porto Rico, and persons in 
naval and military service stationed abroad. The con- 
tinental population is subdivided into states; the states 
into counties; the counties into cities, boroughs or towns; 
the cities into wards; the boroughs and towns into villages 
and rural regions. These civil divisions differ somewhat 
in different parts of the country. 

In comparing the figures for different decades it must be 
remembered that the boundaries of the civil divisions are 
subject to change. State boundaries are quite permanent, 
but cities frequently increase by annexation of suburbs, 
and ward lines change still more frequently according 
to political exigencies. In most cases changes of bound- 
aries are indicated in the census reports by explanatory 
notes. 

In sending to the Director of the Census for reports of 
populations by states or for the whole country, the request 
should be made for that report which gives the facts by 
*' minor civil divisions." 

The enumeration schedule of 19 lo. — In taking the 
census of 1910 the country was divided into 329 supervisor's 
districts each under the charge of a supervisor appointed 
by the President. About 70,000 enumerators were selected 
by the supervisors, or one for about every 1600 persons. 
The enumerators were required to visit each dwelling and 
collect the various statistics included in the schedule. 

The enumerators began their work throughout the 
country on April 15, 1910. The law provided that this 



104 ENUMERATION AND REGISTRATION 

should be completed within two weeks in cities of 5000 or 
more inhabitants, and within 30 days elsewhere. 

The schedule of facts to be collected was printed on sheets 
of paper, 16 by 23 in., on which were 100 horizontal lines, 
50 on each side, and numbered from 1 to 100. The facts 
for each person occupied one line.^ 

The schedule corresponded closely to those used in the 
censuses from 1850 to 1880 and 1900. The schedule used 
in 1890 was somewhat different, a separate schedule sheet 
15 by 11 in. being employed for each family.^ 

For purposes of compilation the facts for each person 
were transferred to a separate punched card. These cards 
were then sorted by machine. 

The data collected by the enumerators for each person 
were as follows: 

At the top of each sheet were given the state, county, 
township or other division of county, name of incorporated 
place, name of institution (if any), ward of city, number of 
supervisor's district, number of enumerator's district, name 
of enumerator and date of enumeration. 



Schedule 
Location. 

Street, avenue, road, etc. 

House number (in cities or towns). 

1. Number of dwelling-house in order of visitation. 

2. Number of family in order of visitation. 

3. Name of each person whose place of abode on Apr. 15, 1910 was in 
this family. [Enter surname first, then the given name and middle 
initial, if any. Include every person living on Apr. 15, 1910. Omit 
children born since Apr. 15, 1910]. 

4. Relation. Relationship of this person to the head of the family. 

1 U. S. Census, 1910, Population, Vol. I, p. 1368. 

2 u. S. Census, 1890, Population, Part I, CCIV. 



THE ENUMERATION SCHEDULE OF 1910 105 

Personal Description. 

5. Sex. 

6. Color or race. 

7. Age at last birthday. 

8. Whether single, married, widowed or divorced. 

9. Number of years of present marriage. 
Mother of how many children? 

10. Number born. 

11. Number now living. 

Nativity. 

Place of birth of each person and parents of each person enumerated. 
If born in the United States give the State or Territory. If of foreign 
birth give the country. 

12. Place of birth of this person (including mother tongue). 

13. Place of birth of father of this person (including mother tongue). 

14. Place of birth of mother of this person (including mother tongue) . 
Citizenship. 

15. Year of immigration to the United States. 

16. Whether naturalized or alien. 

17. Language. Whether able to speak English; or, if not, give 
language spoken. 

Occupation. 

18. Trade or profession of, or particular kind of work done by, this 
person, as spinner, salesman, laborer, etc. 

19. General nature of industry, business or establishment in which 
this person works, ^s cotton mill, dry-goods, store, farm, etc. 

20. Whether an employer, employee, or working on own account. 
If an employee, 

21. Whether out of work on Apr. 15, 1910. 

22. Number of weeks out of work during year 1909. 

Education. . 

23. Whether able to read. 

24. Whether able to write. 

25. Attended school any time since Sept. 1, 1909. 
Ownership of Home 

26. Owned or rented. 

27. Owned free or mortgaged. 

28. Farm or house. 

29. Number of farm schedule. 



106 ENUMERATION AND REGISTRATION 

Miscellaneous. 

30. Whether a survivor of the Union or Confederate Army or Navy. 

31. Whether bUnd (both eyes). 

32. Whether deaf or dumb. 

One has only to read over this Hst to see the importance 
of statistical definitions. What, for example, is meant by 
the " usual place of abode"? This is the place where he 
"lives" or "belongs" or "the place which is his home." 
As a rule it is where he regularly sleeps. And then what 
about those persons who have no place of abode, lodgers 
in one-night lodging houses, tramps, laborers in construction 
camps, etc.? Such persons have to be enumerated where 
found. It required a formidable book of instructions to 
make all these things plain to the enumerators. 

Bowley^s rules for enumeration. — The Enghsh statis- 
tician, Bowley, has laid down the following rules in regard 
to the collection of statistical data by the method of enu- 
meration. 

" In practice the enumerator is usually furnished with 
blanks to be filled out and with questions to be answered. 
These questions should be : 

1. Comparatively few in number. 

2. Require an answer of a number or of a "yes" or "no." 

3. Simple enough to be readily understood. 

4. Such as will be answered without bias. 

5. Not imnecessarily inquisitorial. 

6. As far as possible corroboratory. 

7. Such as directly and unmistakably cover the point of information 
desired. 

These rules apply equally well to the collection of data 
by registration." 

Credibility of census returns. — It is not to be expected 
that the census figures are strictly accurate. Errors are 
bound to be made by the enumerators; some persons are 



COLLECTION OF FACTS 107 

sure to.be omitted from the count, especially those travel- 
ing; some may be counted twice; and in rare instances the 
lists have been thought to be padded. Taken as a whole, 
however, the results may be considered as reliable, and it 
should be noted that the published data of the U. S. Census 
are accepted as evidence which may be introduced without 
proof in courts of record. Unless there is good reason 
for doing otherwise they should be used instead of local 
estimates as the basis of computing vital rates. As a rule 
also they should be used in place of state censuses, but 
there are some exceptions to this. 

Collection of facts by registration and notification. — 
If it is difficult to secure accurate statistics of population 
obtained by enumerators hired for the purpose and properly 
instructed, how much greater the difficulty to obtain com- 
plete and accurate statistics by the method of registration, 
when the returns are made by large numbers of physicians, 
undertakers, clergymen, nurses and laymen not properly 
instructed, not interested in the proceedings and not always 
understanding the law, with inadequate laws, and with 
governments too easy-going to insist on the enforcement of 
such laws as exist! And yet most of the vital statistics of 
the country are collected in this way. Worst of all, the 
people at large do not appreciate the personal importance 
of having the most important events in their lives, — birth, 
marriage and death, — made matters of public record. 

By registration is meant the reporting of certain events 
and associated facts to a governmental authority and the 
official filing or recording of such facts. The reports are 
made in accordance with prescribed rules and usually on 
a blank designed for the purposes. 

Most nations in one way or another have endeavored to 
preserve their history by keeping these personal records. 
In England the registration of baptisms, marriages and 



108 ENUMERATION AND REGISTRATION 

deaths dates back to 1538 when Thomas Cromwell, Vicar 
General under Henry VIH, issued injunctions to all parishes 
in England and Wales requiring the clergy to enter every 
Sunday, in a book kept for the purpose, a record of all 
baptisms, marriages and burials of the preceding week. 
In 1653 this work was assigned to ''parish registers.'' 
It was not until 1837 that registration of births, marriages 
and deaths became a civil function. In 1870 it was made 
compulsory. In parts of Canada the registration of births 
and deaths is still on a parish instead of a civil basis. 

In the early American colonies the practice of recording 
births, marriages and deaths was instituted. In New 
England the town clerk figured largely. In Massachusetts 
a fairly definite law was passed in 1692, according to which 
the town clerk was required to keep such records, and there 
were fees to be paid him for so doing, and penalties for 
those persons who withheld the desired information. This 
act was altered in 1795. In 1842 a registration act was 
passed in Massachusetts which made the Secretary of the 
Commonwealth the custodian of these records. This act, 
together with an amplifying act in 1844, forms the basis of 
registration in Massachusetts to this day. It was brought 
about largely through the activities of Lemuel Shattuck.^ 

The story of the registration of vital statistics is too long 
to be told here. Many physicians, like Dr. Edward Jarvis, 
of Boston, and many committees of such organizations as 
the American Medical Association and the American Public 
Health Associations have played prominent parts in the 
movement. At the present time the United States Bureau 
of the Census is taking the lead in urging necessary reforms 
in the registration of vital statistics. 

The laws relating to the registration of vital statistics are 
not the same in all states. In Massachusetts a State Reg- 
1 State Sanitation, by George C. Whipple, Vol. I, p. 56. 



REGISTRATION OF BIRTHS 109 

istrar in the office of the Secretary of the Commonwealth 
has charge of the matter, but in many states the State 
Board (or Department) of Health has charge. In order to 
bring about uniformity a model law was drafted and en- 
dorsed by a number of national organizations and this has 
been adopted by a number of states. Some of the older 
states, however, still maintain their old arrangement. This 
model law should be carefully studied. It may be found in 
the Appendix. 

Registration of births. — It is important that the birth 
of each and every child born be duly registered. 

The information desired for the legal, social and sanitary 
purposes, according to the United States standard certifi- 
cate approved by the Bureau of the Census, and in use since 
1906, is as follows: 

1. Place of birth, including State, county, township or town, village, 
or city. If in a city, the ward, street and house number; if in a hospital 
or other institution, the name of the same to be given, instead of the 
street and house number. 

2. Full name of child. If the child dies without a name, before the 
certificate is filed, enter the words "Died unnamed." If the living 
child has not yet been named at the date of filing certificate of birth, 
the space for "Full name of child" is to be left blank, to be filled out 
subsequently by a supplemental report, as hereinafter provided. 

3. Sex of child, 

4. Whether a twin, triplet, or other plural birth. A separate cer- 
tificate shall be required for each child in case of plural births. 

5. For plural births, number of each child in order 'of birth. 

6. Whether legitimate or illegitimate. (This question may be omit- 
ted if desired, or provision may be made so that the identity of parents 
will not be disclosed.) 

7. Date of birth, including the year, month and day. 

8. Full name of father. 
9 Residence of father. 

10. Color or race of father. 

11. Age of father at last birthday, in years. 

12. Birthplace of father; at least State or foreign country, if known. 



110 ENUMERATION AND REGISTRATION 

13. Occupation of father. The occupation to be reported if engaged 
in any remunerative employment, with the statement of (a) trade, 
profession, or particular kind of work; (6) general nature of industry, 
business, or establishment in which employed (or employer). 

14. Maiden name of mother. 

15. Residence of mother. 

16. Color or race of mother. 

17. Age of mother at last birthday, in years. 

18. Birthplace of mother; at least State or foreign country, if known. 

19. Occupation of mother. The occupation to be reported if en- 
gaged in any remunerative employment, with the statement of (a) 
trade, profession, or particular kind of work; (b) general nature of 
industry, business, or establishment in which employed (or employer). 

20. Number of children born to this mother, including present birth. 

21. Number of children of this mother living. 

The duty of making out this certificate rests upon the 
attending physician, mid-wife or person acting as such, 
or in their absence upon the father or mother of the child, 
the householder or owner of the premises where the birth 
occurred or the manager or superintendent of the institu- 
tion, pubhc or private, where the birth occurred, each in the 
order named. This certificate must be filed with the local 
registrar within ten days after the date of the birth. A 
supplemental blank is provided in case the child has not 
been named when the first report is submitted. The local 
registrar, or a sub-registrar, must examine this certificate 
as to completeness and probable accuracy, secure correc- 
tions if necessary, keep a record of the birth certificates 
received, numbered serially as received, and once a month 
transmit the original certificates to the State Registrar, for 
permanent preservation. Small fees to local registrars for 
the recording of births are provided and likewise penalties 
for failure. Provision is made for giving certified copies of 
the birth records to persons entitled to receive them. 

The period of time within which a birth must be recorded 
may with advantage be less than the ten days above men- 



ENFORCEMENT OF THE REGISTRATION LAW 111 

tioned, especially in cities, in fact it is best that the birth 
be reported within twenty7four hours. If, as should be 
the case, the local registrar is connected or closely associ- 
ated with the local board of health, the prompt information 
that a birth has occurred enables the health officer to send 
a visiting nurse to offer advice and assistance in caring for 
the child. Infant mortality cannot be greatly reduced in 
cities unless this prompt report is made. 

Advantages to individuals of having births publicly 
recorded. — Legal evidence is thus made available as to: — ■ 

Place of Birth, useful to prove citizenship (necessary for 
pass-ports), to prove residence, to acquire a legal ^' settle- 
ment." 

Time of Birth, useful to prove age, to obtain admission 
to school, to establish right to go to work (legal age), to 
prove liability for military service, to establish right to vote, 
to obtain pensions. 

Parentage, to prove legitimacy, to inherit property, to 
obtain settlement of insurance, to establish citizenship. 

What are some of the evidences of incomplete birth 
registration? — Dr. Louis I. Dublin has suggested three 
simple tests. First. The number of births registered in a 
calendar year should be greater than the number of living 
children under one year of age. Second. The birth-rate 
does not usually vary greatly from year to year. Wide 
and erratic variations indicate probable deficiencies in 
reporting. Third. Birth-rates less than 20 per thousand 
(or less than 25 per thousand in cities which have large 
foreign populations) are uncommon where registration is 
complete. 

Enforcement of the registration law. — The persons most 
concerned in the enforcement of the birth registration law 
are (1) the state registrar, who should be associated with 
the state department of health ; (2) the local registrar, who 



112 ENUMERATION AND REGISTRATION 

should be associated with the local board of health; (3) 
the physician, whose duty it is to make the report; and (4) 
the parents of the child and the child himself or herself. 

In order that better registration be obtained parents and 
physicians should be made to understand the benefits 
which result to individuals and to the community. Facili- 
ties in the form of suitable blanks, etc., should be provided, 
so as not to make the matter of reporting a burden to busy 
physicians. It might well be that a simple post-card 
notification, stating that a birth occurred at such and such 
a place, sent on the day of birth, with a complete certificate 
filed at a later date would help to solve the problem. No 
fee should be given to a physician who does not report 
within the statutory time limit. What is most needed 
however is a rigid enforcement of the penalty clause. A 
local registrar once gave the author as the reason for not 
imposing fines on physicians for failure to report, — "I 
am too good natured." This spirit is fatal to good govern- 
ment. 

Registrars are not without opportunity to obtain evidence 
of neglect. In the case of reported infant deaths the local 
registrar should ascertain if the child's birth had been 
recorded. Church records of baptisms may be compared 
with birth returns. The checks are not as complete as in 
the case of death returns, but an ingenious local registrar 
will have little difficulty in getting good retiirns if he takes 
his task seriously. 

In Cambridge, Mass., the birth records are so incomplete 
that annually a house to house canvass is made to ascer- 
tain the births for the year. This is a disgraceful admis- 
sion of incompetence on the part of the local registrar and 
of the negligence of all concerned. No fines are imposed 
and some of the payments of fees are, with a proper inter- 
pretation of the law, of questionable legality. Unfortu- 



REGISTRATION OF DEATHS 113 

nately Cambridge is not alone in this, but is typical of 
hundreds of other cities. 

Registration of deaths. — The facts desired in connection 
with deaths are as follows, according to the United States 
Standard Certificate. 

1. Place of death, including State, county, township, village, or city. 
If in a city, the ward, street, and house number; if in a hospital or other 
institution, the name of the same to be given instead of the street and 
house number. If in an industrial camp, the name of the camp to be 
given. 

2. Full name of decedent. If an unnamed child, the surname pre- 
ceded by "Unnamed." 

2a. Residence at usual place of abode (ward, street and number), and 
length of residence in city or town where death occurred in years and 
months. Also how long in United States if of foreign birth. 

3. Sex. 

4. Color or race, as white, black, mulatto (or other negro descent), 
Indian, Chinese, Japanese, or other. 

5. Conjugal condition, as single, married, widowed, or divorced. 
5a. If married, widowed, or divorced. Name of husband or wife. 

6. Date of birth, including the year, month, and day. 

7. Age, in years, months, and days. If less than one day, the hours 
or minutes. 

8. Occupation. The occupation to be reported of any person, male 
or female, who had any remunerative employment, with the statement 
of (a) trade, profession or particular kind of work; (b) general nature of 
industry, business, or establishment in which employed (or employer); 
(c) name of employer. 

9. Birthplace; at least State or foreign country, if known. 

10. Name of father. 

11. Birthplace of father; at least State or foreign country, if known. 

12. Maiden name of mother. 

13. Birthplace of mother; at least State or foreign country, if known. 

14. Signature and address of informant. 

15. Official signature of registrar, with the date when certificate was 
filed, and registered number. 

16. Date of death, year, month, and day. 

17. Certification as to medical attendance on decedent, fact and time 
of death, time last seen alive, and the cause of death, with contribu- 



114 ENUMERATION AND REGISTRATION 

tory (secondary) cause of complication, if any, and duration of each, 
and whether attributed to dangerous or insanitary conditions of em- 
ployment; signature and address of physician or official making the 
medical certificate. 

18. Where was the disease contracted if not at place of birth ? Did 
an operation precede death ? If so give date. Was there an autopsy ? 
What test confirmed diagnosis ? 

19. Place of burial or removal; date of burial. 

20. Signature and address of undertaker or person acting as such. 

The first thirteen items are chiefly personal and these 
facts may be signed by any competent person acquainted 
with the facts. Items 16 and 17 comprise the medical 
certificate, which must be made out by the physician, 
if any, last in attendance. In the absence of medical 
attendance the undertaker must notify the local registrar 
who may not issue a burial permit until the case is referred 
to the local health officer for investigation and certifi- 
cation. In case there is suspicion of neglect or unlawful 
act the coroner, medical examiner, or other proper officer 
must conduct an investigation. There are various provisos, 
differing in different states, which should be known by 
every physician and nurse and, of course, by every health 
officer. Finally items 19 and 20 must be signed by the 
undertaker. 

The certificate of death thus made out and duly signed 
must be filed by the undertaker with the local registrar (in 
some states the local board of health), and a burial permit 
or removal permit obtained prior to the disposition of the 
body. This permit must be delivered before burial to the 
person in charge of the place of burial. If the body is 
transported the undertaker must attach a removal permit 
to the box containing the corpse in order that it may reach 
the person in charge of the place of burial. 

Thus the undertaker is primarily responsible for filing 
the certificate with the local registrar (or local board of 



MARRIAGE REGISTRATION 115 

health), but the physician is responsible for making out 
certain very essential parts of the certificate. 

Records of death certificates and burial permits are of 
course kept by the local registrar (or local board of health). 
Thus there is a check on the death certificate, and partly 
for this reason the registration of deaths is more complete 
than the registration of births. It is easier to come into the 
world without public notice than it is to leave it. 

The data regarding the deaths are transmitted by the 
local registrar to the state registrar. 

Uses of death registration. — The uses of death regis- 
tration are legal, economic, and social. It assists in the 
prevention and detection of crime. It is invaluable in the 
settlement of life insurance and property inheritance cases. 
It furnishes the basis of genealogical studies. The sta- 
tistics based upon these records have been a powerful 
weapon in studying disease, and therefore in improving 
the health of the race and lengthening human life. The 
records may be of great local value in the study and sup- 
pression of epidemics and outbreaks of communicable dis- 
eases. 

Marriage registration. — There is no uniform or 
" model " marriage law in the United States; state laws 
differ from each other. The custom is that persons desiring 
to marry must first obtain a civil license from a designated 
local official and present it to the authorized person who 
performs the ceremony. The person officiating is required 
to register the marriage. The persons responsible for mar- 
riage registration are therefore the clergymen and the 
justices of the peace. 

The facts required in the registration of marriages are 
commonly as follows: 



116 ENUMERATION AND REGISTRATION 

1. Date of the marriage. 

2. Place of the marriage. 

3. Names of the persons married. 

4. Their places of birth. 

5. Their residences. 

6. Their ages. ' . 

7. Their color. 

8. The number of the marriage (as the first or second). 

9. If previously married, whether widowed or divorced. 

10. Their occupations. 

11. The names of their parents. 

12. The maiden names of their mothers. 

13. The date of the record. 

14. The signature of the officiating person. 

15. His residence and official station. 

Morbidity registration. — The compulsory registration 
of cases of disease dangerous to the public health is com- 
paratively modern. It is true that many years ago such, 
dreaded diseases as smallpox had to be reported, but it is 
since the organization of modern health departments and 
the general understanding of the manner in which com- 
municable diseases are spread that compulsory notification 
has become widespread. In 1874 the State Board of 
Health of Massachusetts took the lead by arranging a plan 
for the weekly voluntary notification of prevalent diseases. 
Over a hundred physicians agreed to make this report. 
Ten years later, 'in 1884, the state passed a law requiring 
householders and physicians to report immediately to the 
selectmen or board of health of the town all cases of small- 
pox, diphtheria, scarlet fever, or any other disease danger- 
ous to the public health. Other states followed suit. 

' The requirement of notification of diseases is an act of 
police power and authority for it resides in the state gov- 
ernments. In Massachusetts legislative authority has been 
delegated to the State Board (now Department) of Health 
to determine what diseases are dangerous to the public 



MORBIDITY REGISTRATION 117 

health, and such diseases must be reported according to 
prescribed rules. Power is often delegated to local com- 
munities to supplement the state requirements for local 
reports. At the present time the regulations in the several 
states differ greatly from each other. 

In 1913 a model law for morbidity reports was adopted 
by a conference of state and territorial health authorities 
and the U. S. Public Health service. According to this 
law the state boards (or departments) of health are re- 
quired to provide machinery for keeping informed as to 
current diseases dangerous to the public health; physi- 
cians are required to report cases of such diseases imme- 
diately to the local health authorities having jurisdiction; 
teachers in schools must do the same; these records must 
be promptly sent to the state authorities. There are vari- 
ous provisos and provisions for keeping records, and for 
penalties. The data required are the following: 

1. The date when the report is made. 

2. The name of the disease or suspected disease. 

3. Patient's name, age, sex, color, and address. (This is largely for 
purposes of identification and location.) 

4. Patient's occupation. (This serves to show both the possible 
origin of the disease and the probability that others have been or may 
be exposed.) 

5. School attended by or place of employment of patient. (Serves 
same purpose as the preceding.) 

6. Number of persons in the household, number of adults and number 
of children. (To indicate the nature of the household and the prob- 
able danger of the spread of the disease.) 

7. The physician's opinion of the probable source of infection or 
origin of the disease. (This gives important information and frequently 
reveals unreported cases. It is of particular value in occupational dis- 
eases.) 

8. If the disease is smallpox, the type (whether the mild or virulent 
strain) and the number of times the patient has been successfully vac- 
cinated, and the approximate dates. (This gives the vaccination status 
and history.) 



118 



ENUMERATION AND REGISTRATION 



9. If the disease is typhoid fever, scarlet fever, diphtheria, or septic 
sore throat, whether the patient had been or whether any member of 
the household is engaged in the production or handling of milk. (These 
diseases being frequently spread through milk, this information is im- 
portant to indicate measures to prevent further spread.) 

10. Address and signature of the physician making the report. 

Notifiable diseases. — The following was the list of dis- 
eases made notifiable by the model law of 1913. Obviously 
this cannot be a permanent one. It is being continually 
revised chiefly by addition. In many states influenza has 
been added to the list during the last few months (1918). 
Under present conditions the lists vary in different states. 



Group I. — Infectious Diseases. 



Actinomycosis. 

Anthrax. 

Chicken-pox. 

Cholera. Asiatic (also cholera 

nostras when Asiatic cholera 

is present or its importation 

threatened) . 
Continued fever lasting seven days 
Dengue. 
Diphtheria. 
Dysentery : 

(a) Amebic. 

(6) BacHlary. 
Favus. 

German measles. 
Glanders. 

Hookworm disease. 
Leprosy. 
Malaria. 
Measles. 
Meningitis: 

(a) Epidemic cerebrospinal . 
(6) Tuberculous. 
Mumps. 



Ophthalmia neonatorum (con- 
junctivitis of new-born infants) . 

Paragonimiasis (endemic hemop- 
tysis). 

Paratyphoid fever. 

Plague. 

Pneumonia (acute). 

Poliomyelitis (acute infectious). 

Rabies. 

Rocky Mountain spotted, or tick, 
fever. 

Scarlet fever. 

Septic sore throat. 

Smallpox. 

Tetanus. 

Trachoma. 

Trichinosis. 

Tuberculosis (all forms, the organ 
or part affected in each case to 
be specified). 

Typhoid fever. 

Typhus fever. 

Whooping cough. 

Yellow fever. 



INCOMPLETENESS OF MORBIDITY STATISTICS 119 



Group II. — Occupational Diseases and Injuries. 



Arsenic poisoning. 
Brass poisoning. 
Carbon monoxide poisoning. 
Lead poisoning. 
Mercury poisoning. 
Natural gas poisoning. 
PJiosphorus poisoning. 
Wood alcohol poisoning. 
Naphtha poisoning. 

Group III. 
Gonococcus infection. 



Bisulphide of carbon poisoning. 

Dinitrobenzine poisoning. 

Caisson disease (compressed-air 
illness) . 

Any other disease or disability 
contracted as a result of the 
nature of the person's employ- 
ment. 



-Venereal Diseases. 
Syphilis. 



Pellagra. 



Group IV. — Diseases of Unknown Origin. 

Cancer. 



Incompleteness of morbidity statistics. — Complete ac- 
curacy in securing records of morbidity under any law is 
impossible. All of the cases existing are not seen by physi- 
cians, of the cases seen not all are recognized or correctly 
diagnosed, of those recognized not all are reported within 
the required time and some not at all. The chief error is 
that of incompleteness. Conservative physicians wait until 
sure of their diagnosis before reporting. A vast number 
of physicians are careless; a few deliberately shield their 
patients from possible inconvenience by withholding re- 
ports. More and more, however, physicians are coming 
to realize that in dealing with communicable diseases they 
have a public as well as a private duty. Death certificates 
give a partial check on morbidity reports. The ratios be- 
tween statistics oT sickness and death from reportable dis- 
eases furnishes a measure of the incompleteness of the re- 
ports. Trask has noted this difference between morbidity 
and mortality returns ; death records are usually com- 



120 ENUMERATION AND REGISTRATION 

plete but the cause of death often incorrectly diagnosed, 
morbidity records are incomplete, but the diagnosis usu- 
ally correct. This must be kept in mind in dealing with 
fatality ratios. 

Morbidity from non-reportable diseases. — It is much to 
be regretted that at the present time there is no adequate 
way of getting the facts in regard to sickness in the com- 
munity due to diseases which are non-reportable. Sick- 
ness surveys are sometimes made, but they give only the 
facts at a given date, and are, moreover, very expensive to 
make. Hospital records help us a little, the examinations 
made by the life insurance companies help a little, the re- 
cent examinations of men for the army have helped a good 
deal, but some day a more universal method must be de- 
vised. 

Reporting venereal diseases. — For a number of years 
the matter of requiring physicians to report cases of vene- 
real diseases as diseases dangerous to the public health 
has been under consideration by public health officials; 
in a few places it has been attempted. The present war 
has emphasized the need of such reports and these are 
now required in many states. For social reasons it is un- 
desirable to have the names of the victims reported, yet 
under some conditions it is desirable and necessary in the 
control of disease. The following system was adopted by 
the Massachusetts State Department of Health in 1918 as a 
war measure. 

1. Gonorrhoea and syphilis are declared diseases dan-* 
gerous to the public health and shall be reported in the 
manner provided by these regulations promulgated under 
the authority of chapter 670, Acts of 19r3. 

2. Gonorrhoea and syphilis are to be reported (in the 
manner provided by these regulations) on and after Feb. 1, 
1918. 



REPORTING VENEREAL DISEAvSES 121 

3. At the time of the first visit or consultation the physi- 
cian shall furnish to each person examined or treated by 
him a numbered circular of information and advice con- 
cerning the disease in question, furnished by the State 
Department of Health for that purpose. 

4. The physician shall at the same time fill out the num- 
bered report blank- attached to the circular of advice, and 
forthwith mail the same to the State Department of Health. 
On this blank he shall report the following facts: 

Name of the disease. 

Age. 

Sex. 

Color. 

Marital condition and occupation of the patient. 

Previous duration of disease and degree of infectiousness. 

The report shall not contain name or address of patient. 

5. Whenever a person suffering from gonorrhoea or 
syphilis in an infective stage applies to a physician for ad- 
vice or treatment, the physician shall ascertain from the 
person in question whether or not such person has pre- 
viously consulted with or been treated by any other physi- 
cian within the Commonwealth. If not, the physician 
shall give and explain to the patient the numbered circular 
of advice, as provided in the previous regulation. 

If the patient has consulted with or been treated by 
another physician within the Commonwealth and has re- 
ceived the numbered circular of advice, the physician last 
consulted shall not report the case to the State Department 
of Health, but shall ask the patient to give him the name 
and address of the physician last previously treating said 
patient. 

6. In case the person seeking treatment for gonorrhoea 
or syphilis gives the name and^ address of the physician last 
previously consulted, the physician then being consulted 



122 ENUMERATION AND REGISTRATION 

shall notify immediately by mail the physician last pre- 
viously consulted of the patient's change of medical adviser. 

7. Whenever any person suffering from gonorrhoea or 
syphilis in an infective stage shall fail to return to the 
physician treating such person for a period of six weeks 
later than the time last appointed by the physician for such 
consultation or treatment, and the physician also fails to 
receive a notification of change of medical advisers as pro- 
vided in the previous section, the physician shall then 
notify the State Department of Health, giving name, ad- 
dress of patient, name of the disease and serial number, 
date of report and name of physician originally reporting 
the case by said serial number, if known. 

8. Upon receipt of a report giving name and address of a 
person suffering from gonorrhoea or syphilis in an infective 
stage, as provided in the previous section, the State De- 
partment of Health will report name and address of the 
person as a person suffering from a disease dangerous to 
the public health, and presumably not under proper medi- 
cal advice and care sufficient to protect others from infec- 
tion, to the board of health of the city or town of patient's 
residence or last known address. The State Department of 
Health shall not divulge the name of the physician making 
said report. 

Sickness surveys. — , A new method of securing data in 
regard to disease has been recently applied in an experi- 
mental way in a number* of cities, namely that of making a 
house to house canvas to determine the number of persons • 
ill at the time. The Metropolitan Life Insurance Com- 
pany has been foremost in this undertaking under the 
direction of Dr. Lee K. Frankel and Dr. Louis I. Dublin. 
Spring and fall surveys have been made in several cities, 
the enumerator for the most part being the collecting 
agents of the insurance company. 



United states registration area for deaths 123 

The data sheet used included the age, sex, and occupa- 
tion of each member of the family; and if sick the disease 
or cause of disability, its duration and extent, i.e., whether 
confined to bed, and the kind of treatment, i.e., by physi- 
cian at home, hospital, or dispensary. 

Surveys have been made for Rochester, N. Y., September, 
1915; Trenton, N. J., October, 1915; North Carolina 
(sample districts throughout the state), April, 1916; Bos- 
ton, Mass., July, 1916; Chelsea neighborhood of New 
York City, April, 1917; Pittsburg and other cities of 
Pennsylvania and West Virginia, March, 1917; Kansas 
City, Mo., April, 1917. 

This method obviously has its advantages and disad- 
vantages. Within its natural limitations the data secured 
ought to be of value and should furnish an excellent check 
on the results obtained by registration of communicable 
diseases. 

Other methods of securing data. — It will not be pos- 
sible to describe here all of the many ways in which data 
bearing on the health of a community may be secured, 
but mention should be made of the importance of hospital 
records, life insurance records, records of physical exami- 
nations made by the U. S. Army and Navy, records of 
physical examinations of school children. More and more 
the systematic physical examination of the people will be 
extended, until it becomes universal and compulsory. All 
of this will wonderfully increase our knowledge of vital 
statistics. 

United States registration area for deaths. — The Bureau 
of the Census keeps records and publishes reports of the 
mortality of those parts of the United States where the 
statistics are sufficiently accurate to make it worth while 
to do so. A so-called registration area for deaths was es- 
tablished in 1880. This included those states and cities 



124 



ENtJMERATlON AND REGISTRATION 



in which satisfactory registration laws were being effec- 
tively enforced and where there was good reason to believe 
that more than 90 per cent of all deaths were being regis- 
tered. At first the registration area included only two states, 
Massachusetts and New Jersey, and certain cities in other 
states. The area has gradually expanded as shown by the 
following tables. In studying the mortality rates of 
the country in the published reports it is important to keep 
in mind this addition of new territory, new populations, 
from year to year. 



TABLE 19 
REGISTRATION AREA FOR DEATHS 





Population. 


Land 


area. 


Year. 


Number. 


Per cent of 
total. 


Square miles. 


Per cent of 
total. 


(1) 


(2) 


(3) 


(4) 


(5) 


1880 


8,538,366 


17.0 


16,481 


0.6 


1890 


19,659,440 


31.4 


90,695 


3.0 


1900 


30,765,618 


4€.5 


212,621 


7.1 


1901 


31,370,952 


40.3 


212,770 


7.2 


2 


32,029.815 


40.4 


212,762 


7.2 


3 


32,701,083 


40.4 


212,762 


7.2 


4 


33,345,163 


40.4 


212,744 


7.2 


5 


34,052,201 


40.4 


212,744 


7.2 


6 


41,983,419 


48.9 


603,066 


20.3 


7 


43,016,990 


49.2 


603,151 


20.3 


8 


46,789,913 


52.5 


725,117 


24.4 


9 


50,870,518 


56.1 


765,738 


25.7 


1910 


53,843,896 


58.3 


997,978 


33.6 


11 


59,275,977 


63.1 


1,106,734 


37.2 


12 


60,427,247 


63.2 


1,106,777 


37.2 


13 


63.298,718 


65.1 


1,147,039 


38.6 


14 


65,989,295 


66.8 


1,228,644 


41.3 


15 


67,336,992 


67.1 


1,228,704 


41.3 


16 


71,621,632 


70.2 


1,307,819 


44.0 


17 


75,306,588 


72.7 


1,349,506 


45.4 


18 


81,786,052 


77.7 


1,546,166 


52.0 



UNITED STATES REGISTRATION AREA FOR DEATHS 125 



TABLE 20 

LIST OF STATES IN THE REGISTRATION AREA FOR 

DEATHS 



Year of 
Entrance. 


State. 


Year of 
Entrance. 


State. 


(1) 


(2) 


(1) 


(2) 


1880 


Massachusetts 


1906 


South Dakota (drop- 




New Jersey 




ped in 1910) 




District of Columbia 


1908 


Washington 


1890 


Connecticut 




Wisconsin 




Delaware (dropped in 


1909 


Ohio 




1900) 


1910 


Minnesota 




New Hampshire 




Montana 




New York 




Utah 




Rhode Island 


1911 


Kentucky 




Vermont 




Missouri 


1900 


Maine 


1913 


Virginia 




Michigan 


1914 


Kansas 




Indiana 


1916 


North Carolina 


1906 


California 




South Carolina 




Colorado 


1917 


Tennessee 




Maryland 


1918 


Illinois 




Pennsylvania 




Oregon 
Louisiana 



As a result of a test of the completeness of the registra- 
tion of deaths in Hawaii the territory was admitted to the 
registration area for deaths for 1917, thus extending be- 
yond the Continental United States the area from which 
the Bureau of the Census annually collects and publishes 
mortality statistics. The population and land area of 
Hawaii are not included in the figures of the above table. 

The states in which the registration of deaths is still 
too unsatisfactory to warrant inclusion in the registration 
area are: Alabama, Aiizona, Ai-kansas, Delaware, Florida, 
Georgia, Idaho, Iowa, Mississippi, Nebraska, Nevada, 
New Mexico, North Dakota, Oklahoma, South Dakota, 
Texas, West Virginia, and Wyoming. (1918.) 



126 



ENUMERATION AND REGISTRATION 




NEED OF NATIONAL STATISTICS 127 

United States registration area for births. — A regis- 
tration area for births was not established until 1915. For 
this year the Bureau of the Census published its first annual 
report of birth statistics based on registration records. The 
birth statistics published in connection with the regular 
decennial reports from 1850 to 1900 inclusive were based 
on enumerator's returns. 

The registration area in 1915 included only ten states — ■ 
Maine, New Hampshire, Vermont, Massachusetts, Rhode 
Island, Connecticut, New York, Pennsylvania, Michigan, 
Minnesota, and the District of Columbia. In these states 
the registration of births is believed to include upwards 
of ninety per cent of the actual numbers. This registration 
area includes only 10 per cent of the area and 31 per cent 
of the population of the country. In spite of this unfavor- 
able showing a beginning has been made, and inasmuch as 
the standard birth certificate has been adopted for 85 per 
cent of the population and as public sentiment in regard to 
the importance of vital statistics is rapidly gaining ground, 
it is likely that the registration area for births will rapidly 
extend. No state is admitted until the accuracy of its 
records have been submitted to test. 

In 1916 Maryland was added. In 1917, Virginia, 
North Carolina, Kentucky, Indiana, Ohio, Wisconsin, 
Washington, Utah and Kansas were added, bringing the 
population included up to 53.1 per cent. 

Need of national statistics. — More and more it becomes 
obvious that there is need of a national system of keeping 
records of vital statistics, with uniform state laws, and 
with proper provision for the local use of the data regis- 
tered. The excellent work done by the Bureau of the 
Census has done much to emphasize this need. Likewise 
interstate barriers must be broken down in the interest of 
suppressing diseases dangerous to the public health. The 



128 ENUMERATION AND REGISTRATION 

U. S. Public Health Service keeps a record of cases of 
diseases from data furnished by the states and publishes 
the same in its weekly Public Health Reports. This is 
only a part of what is needed. If the time ever comes 
when the United States establishes a real National Health 
Department the maintenance of an adequate system of 
vital records will be one of supreme importance. 

EXERCISES AND QUESTIONS 

1. Compare the methods of numeration used in taking the U. S. 
census of 1910, with those used in 1900, 1890, 1880, etc. 

2. How do these methods compare with those used in England, 
France, Sweden? 

3. Would there be any advantage in making the census date, "as 
of January first "? 

■ 4.- What advantages would come from the adoption of a uniform 
census date for the entire world? 

5. How accurately is the population of China known? 

6. To what extent is the keeping of accurate census records and 
records of vital statistics an index of national progress? 

7. How can improvements be made in ascertaining the facts con- 
cerning morbidity? 



CHAPTER V 
POPULATION 

Estimation of population. — It is only for the census 
years that populations can be known with certainty. For 
the intercensal years, the years between two censuses, it 
is necessary to depend upon estimates. This is also the 
case for the postcensal years, namely, the years following 
the last census. These estimates are only approximately 
true, a fact which must not be forgotten, but they are 
sufficiently near the truth for many practical uses. 

Estimations of population may be made in various ways. 
The natural growth of population is like that of money at 
compound interest except that the interest is being added 
constantly instead of semi-annually or quarterly. Mathe- 
maticians call this geometrical progression. With a given 
constant rate of interest money in the bank increases more 
and more each year. It is the same with population. In 
geometrical progression the basis of our population estimates 
is the annual rate of increase. When dealing with very 
large populations, and especially when dealing with popu- 
lations not influenced by emigration or immigration, this 
method is the most accurate one to use. It has several 
practical disadvantages, however, and in the present shift- 
ing condition of the world's population there are not many 
places where the natural growth of population is the only 
factor to be considered. 

A simpler method is that of arithmetical progression, 
which assumes a constant annual increment between two 

129 



130 POPULATION 

census years. The increase in ten years divided by ten gives 
the annual increase. This is practically the method by which 
money increases by simple interest. The arguments in 
favor of this method of estimating population are that it is 
simple and easily understood; that in view of the various 
disturbing factors due to migration and other causes it gives 
results practically as near the truth as those obtained by 
geometrical progression; that the estimates for the whole area 
of a given district will be equal to the sum of the estimates 
for all the parts of the district, which would not be the case 
with the geometrical method. The U. S. Bureau of the 
Census has adopted this method, and in the interest of uni- 
formity all cities and states should do the same. The 
method is one which should not be extended far into the 
future. In vital statistics it is not necessary to extend it 
beyond ten years from the last census, for ten years always 
brings another census. ; 

Another method is that of using local data as indices — 
such as the number of registered voters, the number of new 
building permits, the number of school children, the number 
of names in the directory, the bank clearings, the number of 
passengers carried by the trolley cars, etc. These facts are 
often obtainable for each year and serve as valuable checks 
on the census method, but as a rule they should not be 
depended upon alone. Common sense must be used. What 
is wanted are the facts, and rigid adherence to a rule when 
the result is manifestly unfair is absurd. When deviations^ 
from accepted practice are made, however, a statement of 
the method of making the estimates of the population 
should always accompany the result. Even the U. S. Census 
utilizes local data to modify its estimates where plainly 
necessary.. 

Estimates of population might be made from records of 
births and deaths if these were accurately kept and if the 



ADJUSTMENT OF POPULATION TO MID-YEAR 131 

migrations of the people were known. Practically this 
method is useless. 

One item in connection with the estimation of the popula- 
tion of cities should not be lost sight of, namely, that of 
changing boundaries. Cities often grow by extending their 
area. Increases of population from this cause should not 
be mistaken for natural increase in population. 

Arithmetical increase. — Let us assume that the popu- 
lation of a place in 1900 was 70,000 and in 1910, 100,000. 
The increase was, by the arithmetical method, 30,000 in ten 
years, or 3000 in each year. For 1904, therefore, the esti- 
mated population would be 70,000 plus four times 3000 or 
82,000; and for 1915 it would be 100,000 plus five times 
3000 or 115,000. It is assumed that within the ten years 
following the last census the annual increase will be the same 
as the average annual increase between the last two censuses. 
This is the simple and customary way of making the estimates. 

It must be remembered that between these particular 
censuses the interval was not exactly ten years. The census 
of 1900 was '^as of June 1st," that of 1910 "as of April 15th." 
Consequently, the interval was ten years less a month and 
a half or 9| years ( = 9.875 years). The average increase was 
not, therefore, 3000 per year, but 30,000 -^ 9.875 or 3038. 
This would make the estimated population 82,152 for 1904 
and 115,190 for 1915. It will be seen that this difference 
is. not great. Nevertheless, it is a correction which in some 
cases is of importance. Whether it will have to be made 
after the next census will depend upon the date decided 
upon. Strictly speaking, the populations of the census 
years should be adjusted to the middle of the year before 
the average annual increments are computed. 

Adjustment of population to mid-year. — The census of 
1910 was "as of April 15th." What then was the population 
on July 1st? 



132 POPULATION 

On June 1, 1900, the population was 70,000. The av- 
erage annual increase was 3038 per year, or 3038 -v- 12 = 
253 per month. On July 1, 1900, the population was, 
therefore, 70,000 + 253 = 70,253. On July 1, 1910, it was 
100,000 + 253 X 2i months or 100,633. The increase in 
ten years was, therefore, 100,633 - 70,253 = 30,380, or 3038 
per year, as before. 

This arithmetical method, therefore, is used in adjusting 
the population for the census years from the day on which 
the census was actually taken to the mid-year. 

For example, on June 1, 1900, the population of the state 
of Indiana was 2,516,462; on Apr. 15, 1910, it was 2,700,876, 
an increase of 184,414 in 118.5 months. On July 1, 1910, 
i.e., 2.5 months later than the census date, the estimated 

2 5 

population would therefore be 2,700,876 + r-^ X 184,414 

or 2,704,767. This is the figure used by the U. S. Census in 
the Mortality Report of that year. 

Geometrical increase. — A simple rule for computing 
populations by the geometrical method is to use the loga- 
rithms of the populations concerned in the same way that 
the populations are used in computing by the arithmetical 
method. Let us assume, as before, that the population was 
70,000 in 1900 and 100,000 in 1910. The logarithm of 
100,000 is 5.0000, that of 70,000 is 4.8451. Instead of sub- 
tracting 70,000 from 100,000 we subtract 4.8451 from 5.0000 
and get 0.1549. Instead of dividing 30,000 by 10 we divide 
0.1549 by 10 and get 0.01549. Then we multiply this by 4 
and get 0.0620. Finally, we add this to 4.8451, which is the log 
of 70,000, and get 4.9071 . This is the log of the answer, which 
is 80,750. The following comparison ought to make this clear : 

Example. — The population of a city in 1900 was 70,000 
and in 1910, 100,000. What was the population in 1904, 
in 1915 and in 1925? 



FORMULA FOR GEOMETRICAL INCREASE 



133 





TABLE 21 






Arithmet- 
ical method. 


Geometrical n 


:ethod. 


(1) 


(2) 


(3) 


Population in 1910. . 
'' 1900.. 


100,000 
70,000 


log of 100,000 
" " 70,000 


= 5 0000 
= 4.8451 


Increase in 10 years- 
Increase in 1 year. • 


30,000 
3,000 




0.1549 
0.0155 


Increase in 4 years. . 


12,000 




0620 


Population in 1900. . 
/' 1904.. 


70,000 
82,000 


log of 80,750 


4.8451 
= 4 9071 


Increase in 5 years. . 

Population in 1900. . 

" 1915.. 


15,000 
100,000 
115,000 


log of 119,500 


0.0775 

5.0000 

= 5.0775 


Increase in 15 years. 
Population in 1900. . 


45,000 
100,000 




0.2325 
5.0000 


'' 1925.. 


145,000 


log of 170,800 = 


= 5.2325 



It will be noticed that for intercensal years the arithmet- 
ical method gives higher estimates than the geometrical, 
but that for postc^nsal years the geometrical results are 
higher. This is illustrated graphically b}^ Fig. 30. 

Formula for geometrical increase. — The mathematical 
formula for geometrical increase is 

Pn = Pc (1 + r)", 

in which Pc is the population at one census, Pn is the 
population n years after P^ r is the annual rate of increase 
and n is the number of years. 

Let us apply this to the case already considered. Here 
we know the two populations P^ and Pn, 70,000 and 100,000, 



134 



POPULATION 




Fig. 30. — Example of Arithmetical and Geometrical Methods 
of Estimating Population. 



FORMULA FOR GEOMETRICAL INCREASE 135 

and we know that n is 10 years; first we need to find r, 
the annual rate of increase. According to algebra we may 
rewrite the above formula, thus: 

log Pn — log Pc = n log (1 + r). 

Substituting the values of the logarithms of 100,000 and 
70,000 and the value of n we have 

5.0000 - 4.8451 = 10 log (1 + r) 

0.1549 = 10 log (1 +r) 

0.01549 = log (1 + r) 

and from the tables of logarithms (1 + r) is found to be 
1.036, hence r = 1.036 - 1 = 0.036, or 3.6 per cent. There- 
fore, the average annual rate of increase between 1900 and 
1910 was 3.6 per cent. 

Knowing this rate and asiKiming it to be constant we can 
find the population in any other year. Suppose we try 
1925, 15 years after 1910. Then we have: 

Pn = 100,000 (1 + 0.036) ^^ 
log Pn = log 100,000 + 15 log 1.036 

= 5.0000 + 15 X 0.01549, 
logPn = 5.23245, 
.*. Pn = 17,079 (according to the log. tables.) 

By the use of this formula many interesting problems can 
be solved. For example, how many years would it take the 
population in our now familiar example to reach 200,000? 
We know that the average rate of increase between 1900 and 
1910 was 3.6 per cent. Therefore, we have in the formula 

200,000 = 100,000 (1 + 0.036) ^ 
We want to find the value of n. We have 

log 2000,00 = log 100,000 + n log 1.036, 
5.30103 = 5.0000 + n X 0.01549, 
0.30103 = n X 0.01549, 

0.30103 ,^,^ 
^ = 001549 = ^^-^^ ^^^''' 



I 



136 POPULATION 

Strictly speaking, we have no reason to use a year or even 
a month as the basis of compounding, as the population is 
increasing from day to day and from hour to hour. A more 
accurate formula may be found in books on calculus. We 
do not need to use it in this work. 

Rate of increase. — The population of the United States 
on June 10, 1900, was 75,994,575; on Apr. 15, 1910, it was 
91,972,266. The increase in 9f years was 15,977,691 or, 
134,833 per month, assuming the increase to have been 
constant. We might divide this still further and say that 
the average increase was 4494 per day, or about 3.12 persons 
per minute. On this basis we might also by computation 
ascertain that the population of the United States passed the 
one hundred million mark at 4 o'clock on Apr. 3, 1915. 
Such statements as this have a fascination for certain people, 
but they are of idle moment. They merely serve to illustrate 
the method of computation by the arithmetical method. 
Had the geometrical method been used the result would have 
been different. As a matter of fact no one will ever know 
just when the population passed the hundred million mark. 

If we take the above figures for 1900 and 1910 and regard 
them as representing a ten year period (instead of 9.875 

years), the increase amounts to ^ ' ' ^^ , or 21 per cent. 

We may divide this by 10 and say the annual increment was 
2.1 per cent, or more accurately by 9.875 and say that it was 
2.13. But we ought not to use the word rate in this connec- 
tion. As a matter of fact, if the rate of increase in 10 years 
was 21 per cent, the average annual rate would not be 2.1 
per cent. If in the formula for geometrical increase we let 
Pc = 100 and Pn = 121, which would represent an increase 
of 21 per cent in 10 years, then 

log 121 - log 100 = 10 log (1 + r), 
2.08278 - 2.00000 = 10 log (1 + r), 



DIFFERENCE BETWEEN ESTIMATE AND FACT 137 



from which 



r = 1.92 per cent, not 2.1 per cent. 



This assumes that, as we might say, the interest is com- 
pounded annually. 

This error of dividing the percentage increase in 10 years 
by 10 to find the annual increase i^ sometimes made in using 
the geometrical method of estimating increase. Obviously 
with compound interest a lower rate suffices to produce a 
given increase in 10 years than with simple interest. The 
proper way to find the annual rate is by the use of the 
formula. 

Decreasing rate of growth. — It seems to be generally 
true that as cities become larger their annual rate of growth 
decreases. A study of six American cities gave the following 
annual rates of increase when the populations were as 
indicated. 

TABLE 22 
DECREASING RATE OF GROWTH OF CITIES 



Stage of 


Annual percent- 


Population 


age Increase. 


.(1) 


(2) 


100,000 


4.85 


200,000 


3.59 


300,000 


2.91 


400,000 


2.48 


500,000 


2.02 


600,000 


1.75 


700,000 


1.66 


800,000 


1.58 



Difference between estimate and fact. — In estimating 
the population either by the arithmetical or geometrical 
method we are assuming something which is almost never 
true, z.e., that the population is increasing regularly. As a 



138 POPULATION 

matter of fact the increase is not regular from year to year. 
Therefore, any estimate may be erroneous. In the absence 
of the facts, however, we are compelled to resort to the 
method of estimation. Also when we assume that the growth 
in the present decade is the same as in the last decade we 
assume a uniformity of conditions which seldom obtains. 
Let us check a few of our estimates by actual census returns. 

In Cambridge, Mass., the census population was 70,028 
in 1890 and 91,886 in 1900, a gain of 21,858 in the decade. 
If the same increase had continued during the next decade 
the population would have been 113,744. The census of 
1910 was, however, only 104,839. 

In Detroit, Michigan, the population in 1890 was 205,876 
in 1900 it was 287,704, the increase being 79,828. If this 
increment continued regularly the population in 1910 would 
have been 365,532; actually it was 465,766. This of course 
is an extreme case. In most cities the estimates agree fairly 
well with the facts. 

Let us take the case of a larger population, say that of the 
United States. In 1890 the population was 62,947,714, in 
1900, 75,994,575, the decadal increase, 1,304,861. The esti- 
mate for 1910 based on these figures would have been 
89,041,436 by arithmetrical, or 91,723,000 by geometrical 
increase. Actually the population in 1910 was 91,972,266. 
For large populations like this the geometrical method gives 
closer results. 

Revised estimates. — Suppose, however, that as in 
Cambridge, Mass., the census of 1910 showed that the city 
had not grown as fast as in the decade from 1890 to 1900, 
what shall be done with the estimates already made for the 
years 1901 to 1909, inclusive? Obviously they were not 
correct even on the theory of steady increase. Yet they 
have been used as the basis of computing birth-rates and 
death-rates. The answer is that if the discrepancy is large 



POPULATION FROM ACCESSIONS AND LOSSES 139 

the populations for those years should be reestimated and 
the birth-rates and death-rates recomputed. Let us. see 
what differences would result. 



TABLE 23 
REVISION OF POPULATION ESTIMATES 



Year. 


Census. 


Postcensal estimate 
based on 1890-1900. 


Intercensal estimate 
based on 1900-1910. 


(1) 


(2) 


(3) 


(4) 


1890 
1900 

1 

2 

3 

4 

5 

6 

7 

8 ' 

9 
10 


70,028 
91,886 

104,839 


94,072 
96,258 
98,444 
100,630 
102,816 
105,002 
107,188 
109,374 
111,560 


93,181 

94,476 

95,771 

97,066 

98,361 

99,656 

100,951 

102,246 

103,541 



Ordinarily the errors are not as great as this and no 
correction need be made, but the chance of error is so great 
that old published figures for death-rates should not be 
accepted at their face value until the population estimates 
have been carefully examined for errors of this sort. 

It would be sound practice to revise all rates based on 
postcensal population estimates every ten years, i.e., after 
each new census. 

Estimation of population from accessions and losses. — 
In a place where records of the births and deaths are accu- 
rately kept it would be possible to use them in estimating 
population, but emigration and immigration enter as dis- 
turbing factors. Two examples of this method will illustrate 
the way in which this method works out. 



140 POPULATION 

In England and Wales the data were as follows: 

Population in 1891 29,000,000 

Births, 1891 to 1901 9,160,000 

38,160,000 
Deaths, 1891 to 1901 5,560,000 

Computed population in 1901 32,600,000 

Census gave, for the year 1901 32,530,000 

Difference representing excess of emigration over 

immigration 70,000 

In Massachusetts the population for 1910 computed in 
this way was 3,092,349, but the census gave 3,366,416, an 
excess of 274,067, which re{)resented in part the excess of 
immigration over emigration and in part, no doubt, incom- 
plete registration of births. 

Estimation of future population. — For some purposes, 
as, for example, in planning for sewerage or water supply 
systems, it is necessary to estimate the population of a city 
for half a century or more in the future. This cannot be 
safely done by mathematical methods alone, for much depends 
upon other things not subject to definite analysis. Bound- 
aries may change, business and manufacturing may expand 
or contract in ways unforeseen, changes in transportation or 
in methods of housing may influence the problem. Mathe- 
matical analyses are helpful, but the conclusions must be 
tempered with judgment based on a study of local conditions 
and on the history of other cities similar in size and conditions. 

A few examples of unfulfilled estimates may be mentioned. 
In 1865 Jas. P. Kirkwood, a well known civil engineer, 
estimated that the population of Cincinnati would be 
431,644 in 1890; actually it proved to be 297,000. 

At Rochester an estimate made in 1889 claimed that the 
population in 1910 would be 283,459; actually this city grew 
to 218,149. At Winnipeg in 1897 a certain estimate of the 



GRAPHICAL METHOD OF ESTIMATING POPULATION 141 

probable population in 1907 was made, but when 1907 
arrived the population was double the estimated figure. 

For long-time estimates the methods already described 
may be used, but with this difference that the rate of past 
increa'se is best obtained, not by taking the results of the 
last two censuses only, but by considering a longer period. 
To look farther ahead than 10 years you must begin farther 
back. This is an important principle which applies to many 
things in fife. It means the use of experience. The pubUc 
health student who desires to project himself forcefully into 
the coming era needs to study the past history of the health 
of the human race. It is equally true in the fields of science, 
philosophy and religion. 

As a rule in United States cities the arithmetical method 
gives results which are too low, and the geometrical method 
gives results which are too high. All things considered the 
graphical method is the most serviceable for long term esti- 
mates as it enables data for various cities to be brought 
together. 

Immigration. — The irregular effect of immigration in 
the United States may be inferred from Fig. 31, which 
shows the immigration by years from 1820 to 1909. Immi- 
gration has occurred in a series of waves, resulting from the 
relative economic conditions in this country and abroad. 
When this incoming population has been concentrated in 
manufacturing cities, as has periodically been the case, it has 
been followed by ^n increased prevalence of disease. The 
subject is, therefore, an unportant one for sanitarians to 
consider. 

The data for immigration are published in the annual 
reports of the U. S. Commissioner General of Immigration. 

Graphical method of estimating population. — The simp- 
lest method of estimating future populations graphically is 
to plot the populations on cross-section paper using all past 



142 



POPULATION 



records available, and then sweep the curve forward accord- 
ing to its general trend. It is easy to use poor judgment in 
doing this. Local conditions should be kept in mind and 
especially additions of area should be considered. 



i,aoo,ooo 


















(\ 




1,100,000 

1,000,000 

900,000 




















i 
















































800,000 
700,000 


















\l 


















^ 




1 
























a 

a 

6B 600,000 

a 
s 


































t 


A 






500,000 
400,000 
300,000 
200,000 
100,000 















\ 


\ 


/ 1 












/\ 




l\ 






\ 


1 












/ 




li 


ll 




i 




J 










/ 






J 


1 




'11 










J 


lA 


/ 


u 


' 




1 






yvsA/ 


M 




\J 




«• 









1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 

Fig. 31. — Immigration to the United States: 1820-1917. (From 
report of Commissioner of Immigration.) 

A safer way is to plot not only the populations for the city 
being considered, but for other cities where the conditions 
are near enough to warrant them being taken as guides. 



GRAPHICAL METHOD OF ESTIMATING POPULATION 143 

These cities must be larger than the one for which the esti- 
mate is to be made. 

A good way is to plot them all on cross-section paper on 
the same scale and then trace the lines upon a single sheet, 
adjusting the. time scale so that all of the curves meet and 
cross on some selected year, usually the last census year. In 
this way there will be a number of population lines extending 
ahead and these may be used as guides in sweeping in the 
curve of the city being considered. 

Judgment inevitably plays a large part in long-term esti- 
mates and statistics are used merely as an aid to that 
judgment. 

Example. — Estimate th'e future population of Springfield, 
Mass., using for comparison the cities of Worcester, Mass., 
Syracuse, N. Y., Rochester, N. Y., and Providence, R. I. 
From the census reports we have the following data: 



TABLE 24 
POPULATION OF CITIES 



Year. 


Springfield. 


Worcester. 


Syracuse. 


Rochester. 


Providence. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


1860 


15,199 


24,960 


28,119 


48,204 


50,666 


1870 


26,703 


41,105 


43,051 


62,386 


68,904 


1880 


33,340 


58,291 


51,792 


89,366 


104,857 


1890 


44,179 


84,655 


88,143 


133,896 


132,146 


1900 


62,059 


118,421 


108,374 


162,608 


175,597 


1910 


88,926 


145,986 


137,249 


218,149 


224,326 



These data are first plotted as in the upper part of Fig. 32. 
They are afterwards brought together as in the lower part of 
the figure, the lines being made to cross on the line of 1910. 
The estimate for Springfield is made by sweeping the curve 
forward as shown. 



144 



POPULATION 



200,000 



.o 150,000 

I— H 

p 100,000 



50,000 




250,000 



o 200,000 

i— I 



o a5o,ooo 



100,000 



50,000 









GRAPHICAL METHOD 

OF 

ESTIMATING THE FUTURE 

POPULATION OF 
SPRINGFIELD, MASS. 




•:a 



^^^ 






' ^ Lines o'oss at Pcpulation 
of Sprinerfleld, lie. 88926 









^ 



Fig. 32. — Example of Graphical Method of Estimating Future 

Population. 



ACCURACY OF STATE CENSUSES 145 

Accuracy of state censuses. — The U. S. Bureau of the 
Census does not recognize as generally acceptable the results 
obtained by those states which enumerate their populations 
in the years which end in 5, on the ground that it does not 
control such intermediate censuses and has no way of assur- 
ing itself of their accuracy. On the whole this position is 
probably sound. In Massachusetts, the last federal census 
in 1910 was made by the same state authority, namely the 
Director of the Massachusetts Bureau of Statistics, which 
has made the state census, and one census is presumably as 
accurate as the other. 

In the past, however, the state censuses have evidently 
not been as accurate as the federal censuses. If the results 
of the federal censuses for Massachusetts are plotted the 
points fall on quite a smooth and regular curve from 1820 to 
1910, the only important departure being during the decade 
of the Civil War. The figures for the state censuses do not* 
all fall on this line, but rise and fall irregularly. This is 
presumptive, though not conclusive, proof of the inaccuracy 
of some of the figures (Fig. 33). 

The Massachusetts state census was taken on May 1 
from 1855 to 1905, inclusive; in 1915 it was taken on 
April 1. 

The question often comes up for decision, shall the state 
censuses be used in estimating populations for the years in the 
last half of each decade ? For the sake of uniformity it is best 
to use the federal figures only. But these figures should, of 
course, be modified if the state census reveals that there 
have been important changes in conditions. The state 
figures should be used, therefore, as a check on the estimates 
based on the federal results. Should glaring differences be 
noticed their cause should be investigated. If state figures 
are used this fact should be stated in connection with the 
estimate. 



146 



POPULATION 



Urban and rural population. — It is common to classify 
the population of a country into ''urban" and ''rural." 
This is done for purposes of discussion, the idea being to 
separate the people living in sparsely settled regions and 
small villages from those living in cities, on the theory that 



4,000,000 



3,000,000 



2,000,000 



1.000,000 





































/ 


































/ 


r 
































y 


/ 
































A 


/ 
































^ 


/ 


































/ 


































/ 


































/ 
































' J 


V 


> 
































Y 






























,<^ 


<:>' 


/ 




















■ 








< 


>y 






























^ 


^ 
































-^ 




















• 


Fe 


Jen 


LlO 


jnsi 


:S 


























o 


StJ 


ite 


:!eni 


5US 











































1830 1840 1850 1860 1870 1880 1890 1900 1910 

Years 

Fig. 33. — Population of Massachusetts according to Federal and 

State Censuses. (The effect of the Civil War should be noticed.) 

the former lead a more individualistic life, while the latter 
lead a more communal life. In cities for example, water* 
supplies, sewerage systems, food supplies, methods of trans- 
portation and various public utilities are used in common by 
all, while in the country each household has its own well, its 
own garden, its own cesspool, its own means of transporta- 
tion. Thus urban and rural populations are supposed to 
live and work under different conditions. 



URBAN AND RURAL POPULATION 147 

Obviously the sepai'ation of the two classes must be an 
arbitrary one. In the United States prior to the Census of 
1880 the limit of 8000 inhabitants was used. In 1880 it 
became Vecognized that many communities of less than 8000 
inhabitants possessed ''the distinctive features of urban 
life," and accordingly the limit was dropped to 4000, although 
the old limit was used in many of the tabulations of the 
census of that year, and also of the years 1890 and 1900. In 
1900 some comparisons of the two limits were made. It was 
found, for example, that 32.9 per cent of the population of 
the United States would be classed as urban on the basis of 
the 8000 Umit, and 37.3 per cent, on the basis of the 4000 
limit. 

In 1910 the limit was reduced by the Census Bureau to 
2500. The reason for this probably lay in the extension of 
various public utilities, once existing only in the cities of 
larger size, to the smaller communities. In 1910, 46.3 per 
cent of the population were classed as urban on the basis of 
the 2500 limit, but only 38.8 were in cities larger than 
8000. 

One must be careful in drawing conclusions from "urban 
and rural statistics." In the first place, of necessity they 
relate to civil divisions. "Outside of New England," says 
the Census Report for 1900, "there is not much difficulty in 
distinguishing between the urban and rural elements of the 
population, as only dense bodies of population are chartered. 
But in New England a town, which is the usual division of 
the county, is chartered bodily as a city when certain con- 
ditions of population are fulfilled, so that a city may contain 
a considerable proportion of rural population, and, conversely, 
a town may contain a compact body of population of magni- 
tude sufficient to be classed as urban." Evidently then, « 
rural population does not necessarily mean people living in 
isolation, as on a farai. Almost every incorporated town or 



148 POPULATION 

borough has some center, and here people may live under 
communal conditions which may be quite as insanitary as 
those found in cities, with houses close together, with board- 
ing houses, saloons, stables, numerous cesspools, and even 
sewers and public water supplies. -/■ 

Attempts have been made by various writers to make a 
triple separation of the population into "rural," '^village," 
and "urban," using populations of 1000 and 4000 as de- 
markations. These add but little to the value of the statis- 
tics and usually it is best to follow the practice of the Bureau 
of the Census. Populations of 3000 and 5000 have also been 
used as limits between rural and urban. Whatever limits 
are used the possible fallacies inherent in an arbitrary classi- 
fication should be kept in mind. 

In comparing conditions as shown by censuses ten years 
apart there is always likely to be some confusion caused by 
communities which have populations near the limit changing 
from one side to the other. The Bureau of the Census has 
followed this practice: "In order to contrast the proportion 
of the total population living in urban or rural territory the 
territory is classified according to the conditions as they 
existed at each census; but in order to contrast between the 
rate of growth of urban and rural communities it is necessary 
to consider the changes of population for the same territory, 
which have occurred between censuses, and the places in- 
cluded in the urban class are those which have populations 
above the limit at the last census, even though they were 
below the limit at the time of the previous census. 

Since about 1820 the urban population of the country has 
been rapidly increasing, the rural population becoming 
relatively less. This is well shown by the following 
figures : 



URBAN AND RURAL POPULATION 



149 



TABLE 25 

TOTAL AND URBAN POPULATION AT EACH CENSUS: 

1790-1910 

(From U. S. Census, 1900, Vol. 1, Pt. 1, p. LXXXIII.) 











Per cent of 


Census 
year. 


Total population. 


Urban population. * 


Number of 
places. 


urban of 
total popu- 
lation. 


(1) 


(2) 


(3) 


(4) 


(5) 


1790 


3,929,214 


131,472^ 


6 


3.3 


1800 


5,308,483 


210,873 


6 


4.0 


1810 


7,239,881 


356,920 


11 


4.9 


1820 


9,638,453 


475,135 


13 


4.9 


1830 


12,866,020 


864,509 


26 


6.7 


1840 


17,069,453 


1,453,994 


44 


8.5 


1850 


23,191,876 


2,897,586 


85 


12.5 


1860 


31,443,321 


5,072,256 


141 


16.1 


1870 


38,558,371 


8,071,875 


226 


20.9 


1880 


50,155,783 


11,450,894 


291 


22.8 


1890 


62,947,714 


18,327,987 


449 


29.1 


1900 


75,994,575 


25,142,978 


556 


33.1 


1910 


91,972,266 


35,726,720 


778 


38.8 



* Population of places of 8000 or more at each census. 

This is also shown by the increase in the number of large 
cities since 1860. 

TABLE 26 

TABLE . SHOWING THE INCREASE IN NUMBER OF LARGE 
CITIES IN THE UNITED STATES BETWEEN i860 AND 1910 



Number of - 
cities with 
population 
above. 


I860. 


1870. 


1880. 


1890. 


1900. 


1910. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7^ 


25,000 

50,000 

100,000 

500,000 

1,000,000 


32 

15 

8 

2 




50 

24 

13 

2 




77 

35 

20 

4 

. 1 


125 

58 

28 

4 

3 


161 

79 

38 

6 

3 


229 

109 

50 

8 

3 



150 . POPULATION 

Density of population. — By the density of population 
we usually mean the number of persons dwelling upon a unit 
area of land, as a square mile or an acre. It is not to be 
supposed that the persons within this unit area are uniformly 
distributed over it. Usually they are not. The ratio is one 
of convenience, however, and variations of density within 
the area under consideration are tacitly assumed. On the 
catchment area of the Croton river (331 square miles) which 
supplied New York with unfiltered water the population in 
1903 was on an average about 52 per square mile, while on 
the catchment areas of many German streams, where the 
water is filtered before being used the population per square 
mile is often 500 or 800. .Thus the average density expressed 
in this way is a valuable means of comparing the relative 
liability of the water to be contaminated, even though both 
in Germany and on the Croton catchment area the popula- 
tion consists of villages and farms irregularly scattered. 

The average density of the population of the United 
States is steadily increasing. In 1790 it was only 4.5 persons 
per square mile; in 1860 it was 10.6; in 1910 it was 30.9. 
The density varies greatly in the different states. Rhode 
Island has the greatest density. In 1910 it was 508.5 per 
square mile, Massachusetts came next with 418.8, then New 
Jersey with 337.7, Connecticut, 231.3, New York,. 191.2, 
Pennsylvania, 171, Maryland, 130.3, Ohio, 117, Delaware, 
103, and Illinois, 100.6. These were the only states above 
100 per square mile. In Nevada the density was only 0.7 
per square mile. 

The density of population of the United States by counties 
is shown in Fig. 34. 

When we need to know the variations in density more 
accurately we take a smaller unit of area. For the purpose 
of calculating the size of sewers required in a district, or for 
studying the congestion of population in a city the density 



DENSITY OF POPULATION 



151 




152 



POPULATION 



per acre is computed. The population density in cities 
usually increases with their population. In the congested 
portions of cities the density may be several hundred per 
acre, sometimes over a thousand. Fig. 35 shows the den- 
sities of population in the different wards of Boston and 
Cambridge in the year 1910. 

There are two ways in which the density of population 
of a city may be computed. The first and most com- 




100,000 200,000 300,000 400,000 500,000 600,000 
Population 

Fig, 35. — Density of Population by Wards in Boston and Cam- 
bridge, Mass.: 1910. 



mon way is to divide the population by the area in 
acres. This gives the actual density per acre. In Boston, 
for example, in 1910 the population was 686,092, the 
acreage 27,674, and the number of persons on the 
average acre was 24.8. But if we look at the density 
from the standpoint of the people we find that the 
median person lives where the density is about 50 per 
acre and that 10 per cent of the population five where the 
density is 125 per acre, 5 per cent where it is 150. In 



POPULATION OF UNITED STATES CITIES 153 

Cambridge, Mass., the average density per acre is 25.1, or 
practically the same as in Boston. The density for the 
median person is also about the same, i.e., 50 per acre; but 
10 per cent of the population live where it is less than 60 
per acre, and 5 per cent where it is only 100. In no ward 
of Cambridge is the density as great as in five large pop- 
ulous wards of Boston. 

For some purposes, as when we are providing a sewerage 
system, the density per acre is what is wanted, but when 
we are considering the crowded condition of the people it 
is the median density based on population which is needed, 
and the proportion of people living under conditions of 
different congestion. We need also to consider areas as 
small as single blocks. 

Population of United States Cities. — The figures in 
Table 27 will be found useful in computing vital rates. They 
are based on published reports of the U. S. Bureau of the 
Census. 



154 



POPULATION 



TABLE 27 

POPULATION OF UNITED STATES CITIES HAVING, IN 
1910, 25,000 INHABITANTS OR MORE 



(1) 

Alabama 

Birmingham 

Mobile 

Montgomery 

Arkansas 

Little Rock 

California 

Berkeley 

Los Angeles 

Oakland 

Pasadena 

Sacramento 

San Diego 

San Francisco . . . 

San Jose 

Colorado 

Colorado Springs 

Denver 

Pueblo 

Connecticut 

Bridgeport 

Hartford 

Meriden (town) . . 

Meriden (city). . . 

New Britain 

New Haven 

Norwich (town) . 

Stamford (town). 

Stamford (city) . . 

Waterbury 

Delaware 

Wilmington 

District of Columbia 

Washington 

Florida 

Jacksonville 

Tampa 

Georgia 

Atlanta 

Augusta 



1900. 


1910. 


1916 (estimate). 


(2) 


(3) 


(4) 


38,415 


132,685 


181,762 


38,469 


51,521 


58,221 


30,346 


38,136 


43,285 


38,307 


45,941 


57,343 


13,214 


40,434 


57,653 


102,479 


319,198 


503,812 


66,960 


150,174 


198,604 


9,117 


30,291 


46,450 


29,282 


44,696 


66,895 


17,700 


39,578 


53,330 


342,782 


416,912 


463,516 


21,500 


28,946 


38^902 


' 21,085 


29,078 


32,971 


133,859 


213,381 


260,800 


28,157 


44,395 


54,462 


70,996 


102,054 


121,579 


79,850 


98,915 


110,900 


28,695 


32,066 


34,183 


24,296 


27,265 


29,130 


25,998 


43,916 


53,794 


108,027 


133,605 


149,685 


24,637 


28,219 


29,419 


18,839 


28,836 


35,119 - 


15,997 


25,138 


30,884 


45,859 


73,141 


86,973 


76,508 


87,411 


94,265 


278,718 


331,069 


363,980 


28,429 


57,699 


76,101 


15,839 


37,782 


53,886 


89,872 


154,839 


190,558 


39,441 


41,040 


50,245 



POPULATION OF UNITED STATES CITIES 155 



TABLE 27 

POPULATION OF UNITED STATES CITIES HAVING, IN 
1910, 25,000 INHABITANTS OR MORE — (Continued) 



(1) 

Georgia — (Continued) 

Macon 

Savannah 

Illinois 

Aurora 

Bloomington 

Chicago 

Danville 

Decatur 

East St. Louis 

Elgin 

Joliet 

Peoria.-. : 

Quincy 

Rockf ord 

Springfield 

Indiana 

Evansville 

Fort Wayne *V 

Indianapolis 

South Bend 

Terre Haute 

Iowa 

Cedar Rapids 

Clinton 

Council Bluffs 

Davenport 

Des Moines 

Dubuque 

Sioux City 

Waterloo 

Kansas 

Kansas City 

Topeka 

Wichita 

Kentucky 

Covington 

Lexington 

Louisville 

Newport 



1900. 



(2) 



23,272 
54,244 

24,147 
23,286 
,698,575 
16,354 
20,754 
29,655 
22,433 
29,353 
56,100 
36,252 
31,051 
34,159 

59,077 
45,115 
169,164 
35,999 
36,673 

25,656 
22,698 
25,802 
35,254 
62,139 
36,297 
33,111 
12,580 

51,418 
33,608 
24.671 

42,938 

26,369 

204,731 

28,301 



1910. 



(3) 



40,665 
65,064 

29,807 
25,768 
2,185,283 
27,871 
31,140 
58,547 
25,976 
34,670 
66,950 
36,587 
45,401 
51,678 

69,647 
63,933 
233,650 
53,684 
58,157 

32,811 
25,577 
29,292 
43;028 
86,368 
38,494 
47,828 
26,693 

82,331 
43,684 
52,450 

53,270 

35,099 

223,928 

30,309 



1916 (estimate). 



(4^ 



45,757 

68,805 

34,204 
27 258 
2,497,722 
32,261 
39,631 
74,708 
28,203 
38,010 
71,458 
36,798 
55,185 
61,120 

76,078 
76,183 
271,708 
68,946 
66,093 

37,308 
27,386 
31,484 
48,811 
101,598 
• 39,873 
57,078 
35,559 

99,437 

48,726 
70,722 

57,144 

41,097 

238,910 

31,927 



156 



POPULATION 



TABLE 27 

POPULATION OF UNITED STATES CITIES HAVING, IN 
1910, 25,000 INHABITANTS OR MORE — (Continued) 



(1) 

Louisiana 

New Orleans 

Shreveport 

Maine 

Lewiston 

Portland 

Maryland 

Baltimore 

Massachusetts 

Boston 

Brockton 

Brookline (town) 

Cambridge 

Chelsea 

Chicopee 

Everett 

Fall River 

Fitchburg 

Haverhill 

Holyoke 

Lawrence 

Lowell 

Lynn 

Maiden 

New Bedford . . . . 

Newton 

Pittsfield 

Quincy , 

Salem 

Somerville 

Springfield 

Taunton , 

Waltham , 

Worcester 

Michigan 

Battle Creek 

Bay City 

Detroit 

Flint 

Grand Rapids . . . 



1900. 



(2) 



1910. 



287,104 
16,013 

23,761 
50,145 

508,957 

560,892 
40,063 
19,935 
91,886 
34,072 
19,167 
24,336 

104,863 
31,531 
37,175 
45,712 
62,559 
94,969 
68,513 
33,664 
62,442 
33,587 
21,766 
23,899 
35,956 
61,643 
62,059 
31,036 
23,481 

118,421 

18,563 

27,628 

285,704 

13,103 

87,565 



(3) 



339,075 
28,015 

26,247 

58,571 

558,485 

670,585 
56,878 
27,792 

104,839 
32,452 
25,401 
33,484 

119,295 
37,826 
44,115 
57,730 
85,892 

106,294 
89,336 
44,404 
96,652 
39,806 
32,121 
32,642 
43,697 
77,236 
88,926 
34,259 
27,834 

145,986 

25,267 
45,166 

465,766 
38,550 

112,571 



1916 (estimate). 



(4) 



371,747 
35,230 

27,809 
63,867 

589,621 

756,476 
67,449 
32,730 

1-12,981 
46,192 
29,319 
39,233 

128,366 
41,781 
48,477 
65,286 

100,560 

113,245 

102,425 
51,155 

118,158 
43,715 
38,629 
38,136 
48,562 
87,039 

105,942 
36,283 
30,570 

163,314 

29,480 
47,942 

571,784 

54,772 

128,291 



POPULATION OF UNITED STATES CITIES 



157 



TABLE 27 

POPULATION OF UNITED STATES CITIES HAVING, IN 
1910, 25,000 INHABITANTS OR 'M.ORE — (Continued) 



(1) 



Michigan — (Continued) 

Jackson 

Kalamazoo 

Lansing 

Saginaw 

Minnesota 

Duluth 

Minneapolis 

St. Paul 

Missouri 

Joplin 

Kansas City 

St. Joseph 

St. Louis 

Springfield 

Montana 

Butte 

Nebraska 

Lincoln 

Omaha 

South Omaha 

New Hampshire 

Manchester 

Nashua 

New Jersey 

Atlantic City 

Bayonne 

Camden 

East Orange 

Elizabeth 

Hoboken 

Jersey City 

Newark 

Orange 

Passaic 

Paterson 

Perth Amboy 

Trenton 

West Hoboken (town) 



1900. 



(2) 



1910. 



25,180 
24,404 
16,485 
42,345 

52,969 
202,718 
163,065 

26,023 
163,752 
102,979 
575,238 

23,267 

30,470 

40,169 

102,555 

26,001 

56,987 
23,898 

27,838 

32,722 

75,935 

21,506 

52,130 

59,364 

206,433 

246,070 

24,141 

27,777 

105,171 

17,699 

73,307 

23,094 



(3) 



31,433 
39,437 
31,229 
50,510 

78,466 
301,408 
214,744 

32,073 
248,381 

77,403 
687,029 

35,201 

39,165 

43,973 

124,096 

26,259 

70,063 
26,005 

46,150 

55,545 

94,538 

34,371 

73,409 

70,324 

267,779 

347,469 

29,630 

54,773 

125,600 

32,121 

96,815 

35,403 



1916 (estimate). 



(4) 



35,363 
48,886 
41,698 
55,642 

94,495 
363,454 
247,232 

33,216 
297,847 

85,236 
757,309 

40,341 

43,425 

46.515 
165;470 



78,283 
27,327 

57,660 
69,893 

106,233 
42,458 
86,690 
77,214 

306,345 

408,894 
33,080 
71,744 

138,443 
41,185 

111,593 
43,139 



158 



POPULATION 



TABLE 27 , 

POPULATION OF UNITED STATES CITIES HAVING, IN 
1910, 25,000 INHABITANTS OR MORE— {Continued) 



N'ew York 

Albany 

Amsterdam 

Auburn. '. 

Binghamton 

Buffalo 

Elmira 

Jamestown 

Kingston 

Mount Vernon 

New Rochelle 

New York 

Manhattan Borough 

Bronx Borough 

Brooklyn Borough . . 

Queen's Borough 

Richmond Borough . 

Newburgh 

Niagara Falls 

Poughkeepsie 

Rochester 

Schenectady 

Syracuse 

Troy 

Utica 

Watertown 

Yonkers 

North Carolina 

Charlotte 

Wilmington 

Ohio 

Akron 

Canton 

Cincinnati 

Cleveland 

Columbus 

Dayton 

Hamilton 

Lima 

Lorain 



1900. 



(2) 



94,151 
20,929 
30,345 
39,647 

352,387 
35,672 
22,892 
24,535 
21,288 
14,720 
3,437,202 
1,850,093 

200,507 
1,166,582 

152,999 
67,021 
24,943 
19,457 
24,029 

162,608 
31,682 

108,374 
60,651 
56,383 
21,696 
47,931 

18,091 
20,976 

42,728 

30,667 

381,768 

381,768 

125,560 

85,333 

23,914 

21,723 

16,028 



1910. 



(3) 



100,253 
31,267 
34,668 

48,443 

423,715 
37,176 
31,297 
25,908 
30,919 
28,867 
4,766,883 
2,331,542 

430,980 
1,634,351 

284,041 
85,969 
27,805 
30,445 
27,936 

218,149 
72,826 

137,249 
76,813 
74,419 
26,730 
79,803 

34,014 

25,748 

69,067 

50,217 

560,663 

560.663 

181,511 

116,577 

35,279 

30,508 

28,883 



1916 (estimate). 



(4) 



106,003 
37,103 
37,385 
53,973 

468,558 
38,120 
36,580 
26,771 
37,009 
37,759 
5,602,841 

575,876 
1,928,734 
2,634,224 

366,126 
97,881 
29,603 
37,353 
30,390 

256,417 
99,519 

155,624 
77,916 
87,401 
29,894 
99,838 

39,823 
■ 29,892 

85,625 

60,852 

410,476 

674,073 

214,878 

127,224 

40,496 

35,384 

36,964 



POPULATION OF UNITED STATES CITIES 



159 



TABLE 27 

POPULATION OF UNITED STATES CITIES HAVING, IN 
1910, 25,000 INHABITANTS OR MORE— (Continued) 



(1) 

Ohio — (Continued) 

Newark 

Springfield 

Toledo 

Yoimgstown 

Zanesville 

Oklahoma 

Muskogee 

Oklahoma City 

Oregon 

Portland 

Pennsylvania 

Allentown 

Altoona 

Chester 

Easton 

Erie 

Harrisburg 

Hazleton 

Johnstown 

Lancaster 

McKeesport 

Newcastle 

Norristown (borough) . 

Philadelphia 

Pittsburgh 

Reading 

Scranton 

Shenandoah (borough) 

Wilkes-Barre 

Williamsport 

York 

Rhode Island 

Newport 

Pawtucket 

Providence 

Warwick (town) 

Woonsocket 

South Carolina 

Charleston 



1900. 



(2) 



18,157 

38,253 

131,822 

44,885 
23,538 

4,254 
10,037 

90,426 

35,416 
38,973 
33,988 
25,238 
52,733 
50,167 
14,230 
35,936 
41,459 
34,227 
28,339 
22,265 
,293,697 

451,512 
78,961 

102,026 
20,321 
51,721 
28,757 
33,708 

22,441 
39,231 
175,597 
21,316 
28,204 

55,807 



1910. 



(3) 



25,404 
46,921 
168,497 
79,066 
28,026 

25,278 
64,205 

207,214 

51,913 
52,127 
38,537 
28,523 
66,525 
64,186 
25,452 
55,482 
47,227 
42,694 
36,280 
27,875 
,549,008 

533,905 
96,071 

129,867 
25,774 
67,105 
31,860 
44,750 

27,149 
51,622 
224,326 
26,629 
38,125 

58,833 



1916 (estimate). 



(4) 



29,635 

51,550 

191,554 

108,385 

30,863 

44,218 
92,943 

295,463 

63,505 
58,659 
41,396 
30,530 
75,195 
72,015 
28,491 
68,529 
50,853 
47,521 
41,133 
31,401 
1,709,518 
579,090 
109,381 
146,811 
29,201 
76,776 
33,809 
51,656 

30,108 
59,411 
254,960 
29,969 
44,360 

60,734 



160 



POPULATION 



TABLE 27 

POPULATION OF UNITED STATES CITIES HAVING, IN 
1910, 25,000 INHABITANTS OR MORE— (Concluded) 



1900. 



(1) 

SouthCarolina — (Continued) 

Columbia. 

Tennessee 

Chattanooga 

Knoxville 

Memphis 

Nashville 

Texas 

Austin 

Dallas 

El Paso 

Fort Worth 

Galveston 

Houston 

San Antonio 

Waco 

Utah 

Ogden 

Salt Lake City 

Virginia 

Lynchburg 

Norfolk 

Portsmouth 

Richmond . 

Roanoke 

Washington 

Seattle - . 

Spokane 

Tacoma 

West Virginia 

Huntington 

Wheeling 

Wisconsin 

Green Bay 

La Crosse 

Madison 

Milwaukee 

Oshkosh 

Racine. 

Sheboygan 

Superior 



(2) 



21,108 

30,154 

32,637 

102,320 

80,865 

22,258 
42,638 
15,906 
26,688 
37,789 
44,633 
53,321 
20,686 

16,313 
53,531 

18,891 
46,624 
17,427 
85,050 
21,495 

80,671 
36,848 
37,714 

11,923 

38,878 

18,684 
28,895 
19,164 
285,315 
28,284 
29,102 
22,962 
31,091 



1910. 



(3) 



26,319 

44,604 

36,346 

131,105 

110,364 

29,860 
92,104 
39,279 
73,312 
36,981 
78,800 
96,614 
26,425 

25,580 

92,777 

29,494 
67,452 
33,190 

127,628 
34,874 

237,194 
104,402 

83,743 

31,161 
41,641 

25,236 
30,417 
25,531 

373,857 
33,062 
38,002 
26,398 
40,384 



1916 (estimate). 



(4) 



34,611 

60,075 

38,676 

148,995 

117,057 

34,814 
124,527 

63,705 
104,562 

41,863 
112,307 
123,831 

33,385 

31,404 
117,399 

32,940 
89,612 
39,651 
156,687 
43,284 

348,639 
150,323 
112,770 

45,629 
43,377 

29,353 
31,677 
30,699 
436,535 
36,065 
46,486 
28,559 
46,266 



COLOR OR RACE, NATIVITY AND PARENTAGE 161 

Metropolitan districts. — For some purposes the popula- 
tion of a city plus its adjacent suburbs is of more importance 
than that of the city itself. During recent years the growth 
of the suburbs has often been much greater than that of the 
city itself. This subject is discussed in U. S. Census, 1910, 
Population, Vol. I, p. 74.' 

In 1910, New York City had a population of 4,766,883, 
the adjacent territory, 1,863,716, or 39 per cent of the city's 
population. During the last decade the city increased 38.7 
per cent and the adjacent territory 45.5 per cent. 

In Boston the city's population was 560,892, that of the 
adjacent territory, 708,492, or 126 per cent of the city's 
population. 

Classification of population. — One of the greatest mis- 
takes which health officers make is failure to take into 
account the make-up of the population. Two places cannot 
be fairly compared as to death-rate or birth-rate, unless 
the composition of the population in the places is substan- 
tially the same. This point will be emphasized again in 
Chapter VII. 

In many demographic studies it is necessary to take into 
account age, sex, and nationality as primary factors; and at 
times also such matters as marital condition, school attend- 
ance, illiteracy, ownership of homes, occupation, and 
so on. 

It will not be possible in this volume to go into all of these 
classifications. They should be carefully studied, however, 
from the census reports themselves. Every health officer 
should know the composition of the people in the city or 
district under his jurisdiction. 

Color or race, nativity and parentage. — The racial 
composition of the United States has changed materially in 
fifty years. This is well illustrated by Fig. 36. In 1850 
about three-quarters of the people were native whites, now 



162 



POPULATION 



1850 



1860 



1870 





1880 




1900 





1890 




1910 




Fig. 36. — Racial Composition of Population of the United States. 



SEX DISTRIBUTION 



163 



only about one-half. There are great differences in different 
cities and states. 

According to the U. S. Bureau of the Census the popula- 
tion is divided into six classes: (1) white, (2) negro, (3) 
Indian, (4) Chinese, (5) Japanese and (6) '^all others." The 
white population is subdivided into: 

a. Native, native parentage, having both parents born 

in the United States. 
h. Native, foreign parentage, having both parents born 
in foreign countries. 

c. Native, mixed parentage, having one native parent 

and the other foreign born. 

d. Foreign born. 

It is often desirable to subdivide the foreign born accord- 
ing to the count ly from which they came. This is true also 
of the parents. 

Sex distribution. — There are two ways in which the 
sexes are compared, — one is to compute the percentage 
which the number of each sex is of the total population, the 
other is to compute the ratio of males to females. Thus, we 
have the following figures for 1910: 



TABLE 28 
COMPARISON OF SEXES IN THE UNITED STATES 





Per cent. 


Males to 


United States. 


Male. 


Female. 


100 females. 


(1) 


(2) 


(3) 


(4) 


Total population 

Native white, native parentage 

Native white, mixed parentage 

Native white, foreign parentage 

Foreign born white 


51.5 
51.0 
49.6 
50.0 
56.4 


48.5 
49.0 
50.4 
50.0 
43.6 


106.2 
104.1 
98.4 
100.0 
129.3 







164 POPULATION 

In most parts of the country males are in excess, and gen- 
erally speaking the ratio of males to females increases from 
east to west. In only a few states do we find females in 
excess. One of these is Massachusetts, where in 1910 the 
ratio was only 96.6. In Nevada, on the other hand, the 
ratio was 181.5, not very far from two men to one 
woman. 

Sex distribution ought to be studied in connection with age 
distribution. 

Dwellings and families. — A knowledge of the number of 
persons in a dwelling or a family is of sociological interest, 
and it may be of practical use in estimating the population 
of an area the boundaries of which are not coincident with 
any civil division. Here we come again to the difficulty of 
definition. What is a dwelling? What is a family? A 
dwelling-house is considered to be "si place where one or 
more persons regularly sleep." A family is '^a household or 
group of persons who live together, usually sharing the same 
table." This includes both private families, consisting of 
persons related by blood, and economic families. 

The ideal family has been said to consist of a father and 
mother and three children with an occasional grandfather or 
grandmother, aunt or uncle. In the United States in 1910 
the average number of persons to a family was only 4.5, — • 
apparently much smaller than the ideal. The average 
number of persons to a dwelling was 5.2. Figures for differ- 
ent parts of the country are given in Table 29. 

For housing problems it is not enough to know that the 
average number of persons per dwelling is 5.2. This extra 
two-tenths of a person is difficult to place. We need to 
know how many dwellings contain one person, how many 
two persons, and how many three, four, five, six, and so 
on. It is difficult to secure these data. 



AGE DISTRIBUTION 



165 



TABLE 29 
SIZE OF FAMILIES AND HOUSEHOLDS 



Place. 


Persons per 
dwelling. 


Persons per 
family. 


Families per 
dwelling. 


(1) 


(2) 


(3) 


(4) 


United States 


5.2 

5.9 

4.7 
6.0 
6.5 
4.2 
15.6 
30.9 
9.1 
7.2 
4.6 
5.1 


4.5 
4.5 
4.6 
4.5 
4.6 
4.0 
4.7 
4.7 
4.8 
4.6 
4.1 
4.6 


1 15 


Urban 


1.31 


Rural 


1.02 


New England 

Urban 

Rural 


1.33 
1.41 
1.05 


New York City 


3.32 


Borough of Manhattan. . . . 

Boston 

Cambridge, Mass 


6.58 
1.90 
1.57 


Los Angeles, Cal 

Spokane, Wash 


1.12 
1.11 



Age distribution. — We now come to what is a most 
important division of the population, namely separation into 
age-groups. In connection with a study of death-rates and 
causes of death a knowledge of age distribution is funda- 
mental. As a factor in vital statistics it is more important 
than sex or nationality or parentage or occupation or any 
other particular characteristic. 

In taking a census it is impossible to find the exact age of 
every person in a community, and even if this could be done 
it would be impracticable to arrange the people in groups, 
varying by short intervals of time. Infants and young 
children may be grouped by their age in weeks or months, 
but older persons are seldom divided into groups for which 
the time interval is less than one year. Five-year and ten- 
year groups are even more commonly used. In this chapter 
we shall not consider smaller subdivisions than one year. 
The ages of infants will be taken up in the chapter which 
treats of infant mortality. 



166 POPULATION 

Census meaning of age. — If we wish to state a person's 
age in years, using a whole number, we may do so in one of 
two ways; we may give the age as that of the last birthday or 
as that of the nearest birthday. The difference is by no 
means insignificant in the case of children, for the difference 
of half a year would represent a large percentage of the age. 
In some parts of the world the next birthday is often stated 
as the age, an infant being regarded as one year of age even 
though he had been born only an hour. In the Orient age 
has to do also with the calendar year in which the child 
was born. A child born in November might In December 
be called a year old, but after January first might be called 
two years. These curious customs ought to be known by 



Grouping by last Birthdays 
0+ 1+ 2+ 3+ 4 + 



y 



-A ^ A y -^ Y ^ Y ^ 

"v ' 

1 2 8 4 5 

Grouping by nearest Birthda>y8 

Fig. 37. — Age-Grouping by Years. 

those enumerating the ages of persons in the foreign quarters 
of our cities and justify the check question asked by census 
enumerators, namely, the date of birth. 

The last birthday method was used in the United States 
census of 1910, 1900 and 1880; it is the method used in Eng- 
land. In 1890, however, the nearest birthday was used. The 
effect of the definition of age on the age-grouping will be ap- 
parent from the following diagram: The nearest birthday 
method creates confusion in the ages of infants and children 
one year old. If infants include children up to the age of one 
year, then the ''one-year" group must be limited to half a 
year or else there is duplication of those between six months 



ERRORS IN AGES OF CHILDREN 



167 



and one year. The discrepancies in the 1890 figures are 
plainly shown by the following table which gives the per- 
centage distribution of the population under five years of 
age. 

TABLE 30 

PER CENT DISTRIBUTION OF POPULATION UNDER 
5 YEARS OF AGE 



Age in years. 


" Nearest 
birthday." 


" Last birthday." 


1890. 


1880. 


1900. 


1910. 


(1) 


(2) 


(3) 


(4) 


(5) 


Under 1 year 
1 + 

2+ 

3 + 

4 + 


Per cent. 

20.5 
14.1 

22.7 
21.4 
21.3 


Per cent. 

20.9 
18 2 
20 6 
20.0 
20.3 


Per cent. 

20.9 
19.3 
20.0 
19.9 
20.0 


Per cent. 

20.9 
18 6 
20.4 
20.3 
19.9 


Total under 5 years 


100.0 


100.0 


100.0 


100.0 



The small number in the one-year group and the large 
number in the two-year group in 1890 should be noticed. 

Errors in ages of children. — The above table shows that 
even by the last-birthday method the age distribution of 
children in one-year groups was unsatisfactory. Normally 
there are more children under one year of age than between 
one and two years, more between one and two than between 
two and three and more between three and four than between 
four and five. Yet in 1910 the one-year group contained 
fewer than the two-year group, and in 1900 the 3+ year 
group contained fewer than the 4+ year group. 

These discrepancies are due to errors. They are greatest 
in populations where there is much illiteracy and where no 
attempt is made to check the age returns by asking the date 
of birth. Thus we may compare the data for Germany 
(1900) and the negro population of the United States (1910). 



168 



POPULATION 



TABLE 31 

PERCENTAGE DISTRIBUTION OF POPULATION 
UNDER 5 YEARS 



Age, 


Germany. 


United States 
(Negro population.) 


(1) 


(2) 


(3) 


0+ 

1+ 

2+- 
3+ 
4+ 
Under 5 


20.6 
20.3 
20.2 
.19.5 
19.3 
100.0 


20.0 
17.4 
20.6 
20.9 
21.1 
100.0 



Errors due to use of round numbers. — An important 
source of error in age statistics is that of mixing round 
numbers with more accurate figures. In replying to the 
enumerator's questions concerning age most persons will, 
state their age accurately, but some will give the nearest 
round number. An ignorant or careless person who may be 
39 or 41 years old may give his age as 40, a figure which in 
his mind is near enough. This habit is encouraged by ask- 
ing for the ^'nearest birthday" as was done in 1890. In most 
censuses* there are enough instances of this sort to produce 
noticeable concentrations around the ages ending in or 5. 
This is well illustrated by Fig. 38, which shows the popula- 
tion of Massachusetts males in 1905 distributed by groups. 
This error of round numbers is by no means confined to the 
subject of age. It is met with in all sorts of statistical work. 
Dates are often stated as ''the first of the month," or the 
tenth or the fifteenth. These, mixed with more accurate 
statements, may produce abnormal concentrations. Methods 
of adjusting data troubled with these concentrations on the 
round numbers are used by statisticians and are referred to^ 
in Chapter XIV. 



ERRORS DUE TO USE OF ROUND NUMBERS 169 



The U. S. Census Bureau in studying the error due to the 
abnormal use of round numbers has made use of a measure 
termed the ''Index of Concentration." This was taken to 
be the ''per cent which the nmnber reported as multiples of 



20 - 



10 



-1 



n 




n n 














Ln 


" ri 


1 


y 


tI 


1-1 


Pi 
















h- 


-1 


_ 








u 








l\ 


PI 










AGE DISTRIBUTION 

IN 

MASSACHUSETTS 

FROM 1905 STATE CENSUS 

VOLUME 1, POPULATION 

AND SOCIAL STATISTICS, P. 555 


- 


u 


h„ 


p 








u 


[r^ 


-fj- 


-1 



















10 



20 



30 



50 



60 



Age in Years 
Fig. 38. — Age Distribution in Massachusetts. 



70 



5 forms of one-fifth of the total number between ages 23 to 
62 years, inclusive." Thus in the U. S. there were 43 million 
persons aged 23 to 62 years. One-fifth of these would be 8.6 
million. The total number of persons aged 23 to 62 whose 
age was reported as a multiple of 5 was 10.3 million. Hence 
the index of concentration was 10.3 -^ 8,6, or 120. 



170 



POPULATION 



It was found that the index of concentration increased 
directly with the ignorance and iUiteracy. For the native 
white persons it was 112; for foreign born whites, 129; 
for colored persons, 153. It is interesting to compare these 
figures for those of certain other countries. 



TABLE 32 
ERRORS OF REPORTING AGE 




Country. 


Date. 


Index of concen- 
tration. 


(1) 


(2) 


(3)' 


Belgium 


1900 
1901 
1900 
1900 
1901 
1881 
1900 
1897 
1905, 


100 


England and Wales 


100 


Sweden- 


101 


German Empire 


102 


France 


106 


Canada 


110 


Hungary 


133 


Russian Empire 


182 


Bulgaria 


245 







Other sources of error. — Besides ignorance as to age 
there are other sources of error. One of these is deliberate 
under-estimate of age, most conspicuous among middle-aged 
women. Another is over-estimate, most conspicuous among 
the aged. The latter is of relatively little weight, liut the 
former tends to overload the early ages of adult life. 

Age groups. — The primary tabulations of the census 
give the ages of the people by single years. For practical 
use and for application to particular localities it is necessary 
to combine them into groups of five, ten, or twenty years, or 
other groups suitable to particular needs. There appears 
to be no recognized standard of age grouping, and perhaps 
this is not desirable as there are many different uses to which 
the figures are put. 



PERSONS OF UNKNOWN AGE 171 

The U. S. Census states the boundaries of the groups in 
inclusive numbers, such as 0-4; 5-9; 10-14; etc., and not 
in round numbers, as 0-5; 5-10; 10-15. With the original 
age records given in years it is undoubtedly the most exact 
method. 

A grouping largely used in the 1910 census was the fol- 
lowing : 

Under 5 Years 
(Under 1 Year) 
5-9 
10-14 
15-19 
20-24 
25-34 
35-44 
45-64 

65 and over 
Age unknown 

In this arrangement we have one-year groups from ages 
one to five, 5-year groups from ages five to twenty-five, 
10-year groups from twenty-five to forty-five, and above 
that twenty-year groups. 

Persons of unknown age. — One of the puzzling things 
about age distribution is to know how to treat the ''age 
unknown." Usually this number is not large, but in par- 
ticular cases it may be. In 1910 only 0.18 per cent of the 
people of the United States were included in this group, and 
in 1900 only 0.26 per cent. 

One way is to place them in a group by themselves, letting 
the size of the group stand as a sort of test of the accuracy 
of the investigation. On the whole this is probably the best 
thing to do. 

Another way would be to distribute the unknowns pro 
rata through the other groups. But there is really no justi- 



172 



POPULATION 



fi cation for doing so, because the persons of unknown age 
may be confined to certain selected ages, as the very old. 

Redistribution of population. — If the ages of the people 
are tabulated by years it is of course easy to combine them 
into any desired age groups; but if the data are tabulated 
according to one age-grouping and it is desired to ascertain 
the numbers in other age-groups the problem is more difficult. 
Approximate results only can be expected and these can be 
obtained by graphical methods or by computation. 
* For this purpose the summation diagram is most convenient. 
In 1910 the population of Cambridge was as follows: 



TABLE 33 
POPULATION OF CAMBRIDGE, MASS., BY AGE-GROUPS 









Persons less than stated age. 


Age-group. 




Age 








Number. 


Per cent. 


(1) 


(2) 


(3) 


(4) 


(5) 


0-1 


2,323 


L 


2,323 


2.3 


1-4 


8,479 


5 


10,802 


10.4 


5-9 


9,471 


10 


20,273 


19.4 


10-14 


8,892 


15 


29,165 


27.9 


15-19 


8,930 


20 


37,095 


36.4 


20-24 


10,408 


25 


47,503 


46.4 


25-34 


19,175 


35 


66,678 


64.6 


35-44 


15,726 


45 


82,404 


79.6 


45-64 


16,732 


65 


99,136 


95.6 


65-99 


4,642 


100 


104,778 


99.4 


Unknown 


61 




61 


0.6 


Total 


104,839 




104,839 


100.0 



The figures in' column (4) are plotted in Fig. 39. Let us 
suppose that we desire to obtain the number of persons in 
age-group 23-27 inclusive. The diagram shows that about 
43,500 were less than 23 years old and about 53,500 less than 



REDISTRIBUTION OF POPULATION 



173 













































too 




























. 




-- 
































^ 


^ 
















90 






















/ 






































/ 


t 




















80 


















/ 


/ 






































/ 
























TO 
















/ 






































1 


/ 


























60 














/ 






































/ 


1 




























50 












/ 






































) 


i 






























uo 










/ 






































h 


( 
































30 








/ 






































h 


r 


































20 






/ 






































/ 






































10 




/ 






































/ 








































{\ 


/ 
















L 

























10 



30 



30 



40 50 60 

Age in. Years 



80 



90 



100 



Fig. 39. — Age Distribution of Population shown by Summation 
Curve, Cambridge, Mass.: 1910. 



28 years old. The group, therefore, contains 53,500 — 43,500, 
or 10,000. 

In making a complete redistribution of the population in 
new age-groups it is well to check the results by adding them 
together to see that they equal the total. The accuracy of 
the result will depend upon the scale used for plotting and 
the smoothness of the curve. 



174 POPULATION 

We might compute the number of persons in age-group 
23-27 as follows : 

10,408 X f = 4163 
19,175 X t\ = 5753 

9916 

This assumes a uniform age distribution within each age- 
group, which is not strictly correct. 
Redistribution of population for non-censal years. — In 

the case of non-censal years the method of redistribution of 
population is essentially the same as that just described but 
there are three steps to the process. 

The first step is to estimate the total population for the 
year in question by methods already described. 

The second step is to find the percentage distribution of 
the population as it was at the time of the nearest census. 
As a rule the percentage composition of a population by age- 
groups does not change rapidly from year to year. For an 
intercensal year it would be possible to find the percentage 
distribution for both the preceding and following census 
and by interpolation obtain more accurate percentages for 
the intercensal years. The use of the summation curve is 
the most convenient method however. 

The third step is to multiply the estimated total popu- 
lation by the percentage obtained in the second step. 
The feature of this problem obviously lies in the second 
step. 

Let us try to find the age distribution of the population 
of Cambridge in the year 1906. In addition to the above 
figures for 1910 we have also from the census records the 
following figures for 1900: 



PROGRESSIVE CHARACTER OF AGE DISTRIBUTION 175 



TABLE 34 

ESTIMATES OF POPULATION BY AGE-GROUPS FOR A 
NON-CENSAL YEAR: CAMBRIDGE, MASS. 



Age-grcup. 


Number. 


Age. 


Persons less than stated age. 


Number. 


Per cent. 


(1) 


(2) 


(3) 


(4) 


(5) 


0-1 

1-4 

5-9 
10-14 
15-19 
20-24 
25-29 
30-34 
35-44 
45-54 
55-64 
65-99 
Unknown 


2,123 
7,519 
8,343 
7,331 
7,781 

10,588 
9,973 
8,157 

12,377 

• 8,561 

5,028 

3,652 

453 


1 

5 
10 
15 
20 
25 
30 
35 
45 
55 
65 
100 


2,123 
9,642 
17,985 
25,316 
33,097 
43,685 
53,658 
61,815 
74,192 
82,753 
87,781 
91,433 
453 


2.3 

10.5 
19.6 
27.5 
36.0 
47.5 
58.4 
67.3 
78.5 
90.0 
95.5 
99.4 






Total 


91,886 




91,886 









The percentage distribution for 1900 and 1910 are both 
shown on Fig. 40. It will be noticed that the two curves 
coincide for the upper and lower ages, but not for the middle 
ages. For the year 1906 the percentages to be used would 
naturally lie somewhere between the two. 

Progressive character of age distribution. — Among the 
causes of the variation of death-rates from year to year is the 
progressive change in age distribution. We often overlook 
this. We know that individuals grow old, but we forget that 
the 10 year old children of today will be 20 years old ten 
years hence, and 30 years old ten years later and so on. We 
are less wise than the motley fool who said : 

"It is ten o'clock: 
'Tis but an hour ago since it was nine, 
And after one hour more 'twill be eleven; 
And so from hour to hour, we ripe and ripe, 
And then, from hour to hour, we rot and rot; 
And thereby hangs a tale." 



176 



POPULATION 



While the age distribution of a population does not change 
rapidly from year to year yet it does change. This is strik- 
ingly shown by the statistics of Sweden from 1750 to 1900. 



100 



90 



^0 



60 



40 



30 



20 



10 





































' 






































































t 


> — ' 









■~~~ 




p— < 
























/" 






































/ 






































/ 






































/ 


s 




































// 


/ 




































^; 


f 






































f/ 






































I 








































/ 








































r 












































































J 


i 






































/ 






































h 


< 






































/ 






































/ 


5 




































J 


/ 






































/ 








































/ 









































10 



20 



30 



40 50 60 

Age in Years 



70 



80 



90 



100 



Fig. 40. — Percentage Age Distribution of Population, CambridgOj 
Mass., showing slight differences in ten years. 



During this interval there was but little emigration or immi- 
gration, but the birth-rate varied considerably. In Fig. 
41, the population data are plotted for five-year groups and 
for five-year intervals of time; consequently the persons who 



PROGRESSIVE CHARACTER OF AGE DISTRIBUTION 177 

appeared in the 0-4-group at one date would appear in the 
5-9-group five years later, except as losses by death occurred. 
It is interesting to see how the influences which increase or 
decrease the numbers of children produce results which flow 



14.0 




OOOOOOOOOOOOO 

in v^i— COOSOi— l'MCO-^i^«Dt^C0050 

i^ j--i~»t~.i--(» X)cocooocoaD ccoooooS 

Fig. 41. — Age Distribution of the People of Sweden by Five- 
Year Groups: 1750-1900. 

as waves throughout a long life-term. For example, the 
high birth-rate between 1820 and 1825, which caused a peak 
in the 0-4-group in 1825, caused a peak in the 5-9-group in 
1830 and this could be traced for three-score years and ten. 
In the same way the trough in the 0-4 curve in 1810 can be 
followed for sixty years. 



178 



POPULATION 



This same progressive change in age distribution can be 
observed in Massachusetts in spite of the fact that the 
curves are confused by accessions due to immigration. The 
peak in the 0-4-group in 1860 can be followed for fifteen 
years, but after that immigration appears to control. The 
immigration peak seen in the 20-24-group in 1880 can like- 
wise be traced almost to 1910. 

This progressive change of age is very important, for with 
constant specific death-rates for each age it would auto- 
matically control the general death-rate. It shows too that 
a loss of millions of young men in the present Great War will 
profoundly affect the age distribution of the nations of Europe 
for half a century to come. There is much food for reflection 
in this study. 

Tjrpes of age distribution. — According to Sundbarg one 
of the striking features of normal age distribution is the fact 
that about one-half of the population are between 15 and 50 
years of age. He distinguishes three types of age distribu- 
tion. The first is the Progressive Type, the second the 
Stationary Type, and the third, the Regressive Type. These 
are illustrated by the following typical groupings: 



TABLE 35 
TYPES OF POPULATION 



Age-group, 
years. 


Per cent of population. 


Progressivie 

type. 


Stationary 
type. 


Regressive 
type. 


(1) 


(2) 


(3) 


(4) 


0-14 
15-49 
50- 


40 
50 
10 


33 
50 
17 


20 
50 
30 



TYPES OF AGE DISTRIBUTION 



179 



It will be noticed that in all cases, the proportion of middle- 
aged persons is the same, and that the classification depends 
upon the proportion of persons under 15 years of age to 
those more than 50 years of age. 

To these classes might be added two more, one in which 
a population has lost many of its middle-aged persons by 
emigration and one in which a population has gained by 
accessions of middle-aged persons. If the percentage of 
persons between 15 and 50 years of age is much less than 50 
it indicates that the place has lost by emigration and this may 
be termed the secessive type; while if the percentage of per- 
sons between 15 and 50 years of age is greater than 50 it may 
be termed the accessive type. 

The following are examples of age distribution on the basis 
of this classification: 



TABLE 36 
TYPES OF POPULATION BASED ON AGE-GROUPING 



(1) 



Sweden (1751-1900) 

United States (1910) 

Massachusetts 

Minnesota 

New York State 

Washington State 

Maine 

Mass., native white of native parentage 

Mass., native white of foreign or mixed par- 
entage 

Mass., foreign-born white. 



Per cent of population. 



0-14 
years. 



(2) 



33 
32 

27 
32 
27 
26 
27 
28 

46 
6 



15-49 
years. 



(3) 



50 
54 
57 
54 
58 
61 
51 
50 

48 

74 



50 years 
and over. 



(4) 



17 
15 
16 
14 
15 
13 
22 
22 

6 
20 



180 



POPULATION 



It will be seen that Sweden has a normal stationary popu- 
lation, Massachusetts has an accessive population with 57 
per cent between 15 and 50 years. Washington is even more 
accessive. Maine tends to be regressive, as it has an abnor- 
mally large number of persons over 50 years of age. This is 
also the case with the population of native-white parentage 
of Massachusetts. The native-white population of foreign 
or mixed parentage, however, is decidedly progressive. 

Standards of age distribution. — For purposes of com- 
putation and comparison it is often convenient to have some 
standard of age distribution which can be used as a basis of 
reference. Several have been suggested. 

A simple one was the actual population of Sweden in 1890. 
This was suggested because the country was not much in- 
fluenced by emigration or immigration. This standard had 
only five groups. It was this: 



TABLE 37 
AGE DISTRIBUTION OF SWEDEN, 1890 



Age-group. 


Per cent. 




(1) 


(2) 




0-1 
1-19 
20-39 
40-59 
60- 


2.55 
39.80 
26.96 
19.23 
11.46 




100.00 





STANDARD MILLION 



181 



The *' Standard Million," namely the population of Eng- 
land and Wales in 1901, has been much used in adjusting 
birth-rates and death-rates. It is as follows: 



TABLE 38 
ENGLAND AND WALES STANDARD MILLION OF 1901 



Age-group. 


Males. 


Females. 


Persons. 


(1) 


(2) 


(3) 


(4) 


0-5 


57,039 


57,223 


114,262 


&-9 


53,462 


53,747 


107,209 


10-14 


51,370 


51,365 


102,735 


15-19 


49.420 


50,376 


99,796 


20-24 


45,273 


50,673 


95,946 


25-34 


76,425 


85,154 


161.579 


35-44 


59,394 


63,455 


122,849 


45-54 


42,924 


46,298 


89,222 


55-64 


27,913 


31,828 


59,741 


65-74 


14,691 


18,389 


33,080 


75- 


5,632 


7,949 


13,581 



G. H. Knibbs and C. H. Wickens/ statisticians of the 
Commonwealth of Australia have worked out in a very 
elaborate way the probable normal age distribution of the 
people of Europe for the year 1900 or thereabouts. Eleven 
countries are considered. The results were as follows: 

1 The Determination and Uses of Population Norms representing 
the Constitution of Populations according to Age and Sex, and accord- 
ing to Age only, Transactions, 15th International Congress on Hygiene 
and Demography, Vol. VI, p. 352. 



182 



POPULATION 



TABLE 39 
PER CENT OF POPULATION AT EACH AGE 

(Eleven Countries of Europe) 



Age. 


Per 

cent. 


Age. 


Per 
cent. 


Age. 


Per 

cent. 


Age. 


Per 

cent. 


Age. 


Per 
cent. 


(1) 


(2) 


(1) 


(2) 


(1) 


(2) 


(1) 


(2) 


(1) 


(2) 





2.46 


19 


1.90 


38 


1.25 


57 


0.67 


76 


0.20 


1 


2.43 


20 


1.86 


39 


1.21 


58 


0.64 


77 


0.18 


2 


2.41 


21 


1.83 


40 


1.18 


59 


0.62 


78 


0.16 


3 


2.38 


22 


1.80 


41 


1.15 


60 


0.59 


79 


0.13 


4 


2.35 


23 


1.76 


42 


1.11 


61 


0.57 


80 


0.11 


5 


2.33 


24 


1.73 


43 


1.08 


62 


0.54 


81 


0.10 


6 


2.30 


25 


1.69 


44 


1.05 


63 


0.51 


82 


0.08 


7 


2.27 


26 


1.66 


45 


1.02 


64 


0.49 


83 


0.07 


8 


2.24 


27 


1.62 


46 


0.99 


65 


0.46 


84 


0.05 


9 


2.21 


28 


1.59 


47 


0.96 


66 


0.44 


85 


0.04 


10 


2.19 


29 


1.56 


48 


0.93 


67 


0.42 


86 


0.03 


11 


2.15 


30 


1.52 


49 


0.89 


68 


0.39 


87 


0.02 


12 


2.12 


31 


1.49 


50 


0.86 


69 


0.37 


88 


0.02 


13 


2.09 


32 


1.45 


51 


0.84 


70 


0.34 


89 


0.01 


14 


2.06 


33 


1.41 


52 


0.81 


71 


0.32 


90 






15 


2.03 


34 


1.38 


53 


0.78 


72 


0.29 


91 






16 


2.00 


35 


1.35 


54 


0.75 


73 


0.27 


92 




0.02 


17 


1.96 


36 


1.31 


55 


0.73 


74 


0.24 


93 






18 


1.93 


37 


1.28 


56 


0.70 


75 


0.22 


94) 




















All 


ages 


100.0 



Age distribution of the population of the United States. — 

On account of the heterogeneous character of the people 
of the United States, due to immigration and to internal 
migrations, we find that states and cities vary widely in the 
age composition of their inhabitants. In the older parts of 
the country we find a more normal age distribufion of the 
people, one that approaches that of Sweden and Switzerland, 
but in the newer sections, especially in the west, we find an 
abnormally large number of persons of middle-age. This is 
also true of cities to which persons of middle-age are drawn. 
On the other hand the rural districts are relatively low in 
the middle-age groups. There are also important differences 



AGE DISTRIBUTION 

MALES FEMALES 



183 





























































1 


^ . 














... J 

r 

r 

1 — 


1 

1 — 
r 

1 




I 

A 

1 

— — ^— 


1 


\ 

1 


3 
1 

' — ^ 

1 


— -I 

k 

1 


■■■:: 
H 


13 
3 





^ 

^ 




















1 





1^ 10 8 6 1 2 2 4 6 8 10 13 

Hundreds of Thousands 

Fig. 42. — Distribution of Population by Arp and Sex, United 

States, 1910, 



184 



POPULATION 



between native whites, foreign born whites and negroes; 
and between males and females. The student is urged to 
study in the census reports these differences among differ- 
ent classes of populations and in different sections of the 
country. 

The following table shows the percentages of total popula- 
tion in 1910 arranged by years: 



TABLE 40 
PER CENT OF TOTAL POPULATION, BY SINGLE YEARS, 1910 

(United States) 



Age 





10 


20 


30 


40 


50 


60 


70 


80 


90 





2.4 


2.0 


2.0 


2.0 


1.7 


1.2 


0.7 


0.4] 






1 


2.1 


1.9 


1.9 


1.2 


0.9 


0.7 


0.4 


0.2 






2 


2.4 


2.1 


2.0 


1.6 


1.2 


0.9 


0.5 


0.2 


0.3 


* 


3 


2.3 


1.9 


1.9 


1.4 


1.0 


0.7 


0.4 


0.2 






4 


2.3 


2.0 


1.9 


1.4 


0.9 


0.7 


0.4 


0.2. 






5 


2.2 


1.9 


2.0 


1.7 


1.2 


0.7 


0.5 


0.2] 






6 


2.2 


2.0 


1.8 


1.4 


0.9 


0.7 


0.3 


0.2 






7 


2.1 


1.9 


1.7 


1.2 


0.9 


0.5 


0.3 


0.1 > 


0.1 


t 


8 


2.1 


2.1 


1.9 


1.5 


1.0 


0.6 


0.3 


0.1 






9 


2.0 


1.9 


1.5 


1.2 


0.9 


0.5 


0.3 


0.1 







Less than 0.1%. 



t Age unknown = 0.2% 



The concentrations around the years ending in and 5 
should be noticed. The differences between the percentages 
for males and females in the whole population are relatively 
slight. 

EXERCISES AND QUESTIONS 

1. What were the points in the Washington controversy in regard to 
death-rates and population? [See Am. J. P. H., Apr., 1917, June, 
1917, Feb., 1918.] 

2. From the data given in Table 3, 13th Census, Population, Vol. L, 
p. 24, estimate by three methods the probable population of the United 
States in 1950. 



EXERCISES AND QUESTIONS 



185 



3. What was the average annual percentage rate of increase of the 
population of the United States between 1790 and 1800, assuming a 
geometrical rate of increase? Between 1900 and 1910? 

4. Under what temperature conditions do the people of the United 
States live? (See 11th Census, page ix.) 

5. Under what rainfall conditions do the people of the United States 
live? (See 11th Census, page ix.) 

6. From data given on page 314 of the 13th Census, Population, 
Vol. I, make a table giving the age distribution by single years of the 
entire population of the United States, the native white of native 
parentage and the foreign born white. 

7. Make a plot of the last two. 

8. Assuming the age distribution of the United States native white 
population of native parentage (both sexes) as given below, find by 
graphical methods the age distribution as indicated. 



Given 


Wanted 


Age 


Per cent 


Age 


Per cent 


6-4 


13.2 


0-4 


? 


5-9 


11.8 


5-14 


? 


10-29 


21.1 


15-24 


? 


20-29 


17.7 


25-34 


? 


30-39 


13.1 


35^44 


? 


40-49 


9.2 


45-64 


? 


50-59 


6.9 


65-84 


? 


60-69 


4.4 






70-79 


2.1 


• 




80-89 


0.5 







Check the result by computation from figures given in previous 
problems. 

9. Look up the " Incremental Increase Method" of estimating future 
populations. (Jour. Am. Water Works Asso., March, 1915.) 

10. What is meant by the "Center of Population?" Where was 
the centre of population in the United States in 1790? In 1910? [U. S. 
Census, 1910, Population, Vol. I, p. 45.] 

11. What is the "median point " ? 

12. Which states have the largest per cents of urban population? 

13. Describe Moore's " Expectancy Curve," for estimating future 
populations. (Engineering News, Nov. 2, 1916, p. 844.) 



CHAPTER VI 

GENERAL DEATH-RATES, BIRTH-RATES AND MAR- 
RIAGE-RATES 

Gross death-rates (general death-rates.) — Stated sim- 
ply, the death-rate is the rate at which a population dies. 
It is the ratio between the number of persons who die in a 
given interval of time and the median number of persons 
alive during the interval. Unless otherwise specified the 
interval of time is considered to be one year. For the sake 
of comparison the ratio mentioned is reduced to the basis 
of some round number of population, generally 1000. Not 
until such reduction is made may we consider this ratio as 
a '' rate." 

The computation is, of course, very simple. If in the 
year 1917 the number of deaths in a given city was 5710 
and the population on July 1 of that year was 390,000, then 
the death-rate ^as: 

5710 -f- 390,000, or 14.6 for each thousand. 

The death-rate for 1917 was therefore 14.6. /We sometimes 
call this the " general " death-rate because it refers to the 
general population. Sometimes it is called the " crude " 
death-rate to distinguish it from rates corrected and ad- 
justed in various ways.\y Or it may be called the " annual " 
death-rate. This is unnecessary, however, as death-rates 
are always assumed to refer to a year as the basis unless 
stated to the contrary. Perhaps the best term of all would 
be the " Gross death-rate," but this term is not as common. 

186 



PRECISION OF DEATH-RATES 187 

Death-rates may be based on 10,000 or 100,000 or 
1,000,000 of population, but 1000 is the common base for all 
general rates. The higher numbers, however, are often 
used for special rates, as described in the next chapter. 

The method of estimating mid-year population was fully 
described in the preceding chapter. 

Precision of death-rates. — The accuracy of a death- 
rate depends upon the accuracy of the number of deaths 
and the correctness of the estimated population. One or 
both of these may be in error. . Only in a census year can the 
death-rate be computed from actual facts, because only in 
a census year is the population known by actual count. 
In other years, the population is estimated, and hence the 
death-rate based upon it must also be regarded as an 
estimate. Incorrect estimates of population obviously must 
produce incorrect death-rates. If this fact be kept in mind 
it will prevent one from drawing unwarranted conclusions 
in comparing rates which differ from each other by small 
amounts. 

It is quite common to see the gross death-rate, referred to 
1000 persons as a basis, expressed to the second, place of 
decimals. This is warranted in the case of large popula- 
tions for then the figures in the second decimal place have 
a significant value. It is not warranted for small popu- 
lations. This, it will be remembered, was discussed in 
Chapter II, but the following figures will further illustrate 
the point. 

In A, with a population of 1000, the number of deaths 
was 16 and, of course, the death-rate was 16. An error of 
one death, the smallest possible error, would have made the 
deaths 17 (or 15). In B, with a population of 10,000, an 
error of one death would have changed the rate from 16.0 
to 16.1; in C, population 100,000, from 16.00 to 16.01, and 
in D, population 1,000,000, from 16.000 to 16.001. In a 



188 DEATH-, BIRTH- AND MARRIAGE-RATES 

TABLE 41 
PRECISION OF DEATH-RATES 



City. 


Population. 


Number of deaths. 


Death-rate. 




(1) 


(2) 


(3) 


(4) 


A 


1 


1,000 
1,000 


16 
17 


16.00 
17.00 




B 




10,000 
10,000 


160 
161 


16.00 
16.10 




C 


\ 


100,000 
100,000 


1,600 
1,601 


16.00 
16.01 




D 


1 


1,000,000 
1,000,000 


16,000 
16,001 


16.00 
16.001 





city of less than 10,000 population it would obviously be 
unreasonable to use two decimal places. 

Similarly the following figures show the differences in 
population required to change the death-rate from 16.00 
to 16.10 in cities of different size, the actual numbers of 
deatlis remaining the same. 

TABLE 42 
PRECISION OF DEATH-RATES 



City. 


Death-rate. 


Number of deaths. 


Population. 


Difference in 
population. 


(1) 


(2) 


(3) 


(4) 


(5) 


A 


1 


16.00 
16.10 


16 
16 


1,000 
994 


\ 


6 


B 


1 


16.00 
16.10 


160 
160 


10,000 
9,938 


\ 


62 


C 


1 


16.00 
16.10 


1,600 
1,600 


100,000 

99,378 


\ 


621 


D 


I 


16.00 
16.10 


16,000 
16,000 


1,000,000 
993,789 


\ 


6211 



CORRECTED DEATH-RATES 



189 



It will be noticed that in all cases the percentage differ- 
ence in population is the same, i.e., 0.62 per cent. This 
percentage varies^ according to the death-rate. To alter 
the death-rate from 12.00 to 12.10, for example, if the num- 
ber of deaths remained the same, would require a change 
of population of 0.83 per cent. The following figures show 
the percentage change in population required to alter 
the death-rate by 0.10 per 1000 from certain given death- 
rates. 

TABLE 43 



Change of rate from 


Percentage 

change of 

population. 


(1) 


(2) 


20.00 to 20. 10 


0.50 


19.00 to 19.10 


0.52 


18.00 to 18.10 


0.55 


17.00 to 17.10 


0.58 


16.00 to 16.10 


0.62 


15.00 to 15.10 


0.66 


14.00 to 14.10 


0.71 


13.00 to 13.10 


0.76 


12.00 to 12.10 


0.83 


11.00 to 11.10 


0.90 


10.00 to 10.10 


0.99 



As a rough and ready rule we may therefore decide that 
for places smaller than 1000 the death-rate shall be stated 
in whole numbers; for places between 1000 and 100,000 
one decimal shall be used; for places above 100,000 two 
decimal places shall be used. 

Corrected death-rates. — What shall be taken as the 
number of deaths in a community? Shall non-residents 
who die within the geographical limits be included? Shall 
residents who die away from home be referred back to the 
place where they live? In other words shall the place for 
which the death-rate is computed be considered as a geo- 



190 DEATH-, BIRTH- AND MARRIAGE-RATES 

graphical area or as a community of persons? The answer 
must depend upon the use which is to be made of the facts. 

The Bureau of the Census, looking at the matter in a 
broad way, takes the geographical point of view. It can 
hardly do otherwise. By recording deaths in the place 
where the deaths actually occur there is far less danger that 
all deaths will not be recorded and that no death will be 
counted twice than if a process of distribution by actual 
residence were attempted. It may be laid down as a general 
rule that in computing gross death-rates all deaths within 
the defined area shall be included and no others; that is, 
gross death-rates shall have a geographical basis. 

This does not prevent the making of corrections to allow 
for local conditions. Often such corrections are desirable. 
If a hospital is located in a suburban town near a large city 
the deaths in that hospital should be included in the gen- 
eral death-rate of the town; but this figure could not be 
taken as an index of the hygienic or sanitary condition of 
the town. For such a purpose another rate ^ a corrected 
rate — should be computed, leaving out the hospital deaths. 
This might be called the local death-rate. This rate should 
not be used in place of the gross death-rate, but in addition 
to it. 

If, besides the omission of non-resident deaths in insti- 
tutions, the attempt is made to find and include the deaths 
of residents who have died away from home we might call 
the result the " resident death-rate.'' 

The gross death-rate, or general rate, is best for pur-* 
poses of national or state record. The local rate is best for 
environmental studies. The resident rate is useful for 
social and political studies. 

In New York city the health department publishes a 
general death-rate and also a " corrected " death-rate in 
which the deaths are redistributed among the five boroughs 



CORRECTED DEATH-RATES 



191 



on the basis of residence. This is because so many persons 
residing in one borough are taken to hospitals in other 
boroughs. In some cases this makes an important differ- 
ence. For the week ending Mar. 23, 1918, the death- 
rates for the five boroughs were as follows: 

TABLE 44 
DEATH-RATES IN NEW YORK CITY 



Borough. 


General death- 
rate. 


Resident death- 
rate. 


(1) 


(2) 


(3) 


Manhattan 

Bronx 

Brooklyn 

Queens 

Richmond 


20.32 
20.20 
18.98 
20.71 
25.13 


20.30 
17.68 
20.04 
20.98 
18.98 



On the basis of the gross death-rate Richmond is seen 
to have a death-rate much higher than Manhattan, but 
its resident, or " corrected," rate is lower than that of 
Manhattan. 

At the end of a year a preliminary death-rate is often 
computed and published. Afterwards delayed reports of 
deaths are received and this necessitates a correction. The 
term '' corrected " death-rate is sometimes applied to the 
new result. This of course is a proper use of the adjective, 
but a better term would be "final." 

The term " corrected death-rate " has been used by 
some writers as synonymous wdth the " standardized death- 
rate," described on page 240. This use of the term is 
unfortunate and should be avoided. 

Properly the word " corrected " should be applied only 
to death-rates in which changes are made in the number of 
deaths. 



192 DEATH-, BIRTH- AND MARRIAGE-RATES 

Revised death-rates. — Inasmuch as death-rates are 
based on estimated populations in post-censal years, and as 
these estimates are usually less accurate than intercensal 
estimates, it is always wise after each new census to re- 
compute the death-rates for the preceding intercensal years 
if it is found that the new census is different from the 
estimated population. Sometimes the resulting changes 
are slight, but they may be considerable. The rates based 
on these revised estimates of population should be called 
'' revised death-rates.^' 

Variations in death-rates in places of different size. — 
Wide fluctuations in the general death-rates from year to 
year are to be expected in small places. Having a small 
population a change of one death in a year may consider- 
ably alter the rate. In larger populations the fluctuations 
are less marked. This is well illustrated by the death- 
rates of three places in Massachusetts, — Boston (popu- 
lation 686,092 in 1910), Springfield (88,926) and Yarmouth 
(1420). Fig. 43 shows that the death-rate for Boston 
changed slowly, that of Springfield, although lower, fluc- 
tuated more, while that of Yarmouth varied through wide 
limits. 

This very well illustrates what is sometimes called the 
principle of large numbers. 

Errors in published death-rates. — It is necessary to use 
published death-rates and birth-rates with great caution. 
The old reports especially contain many unsuspected errors. 
For example, it was not at all uncommon ten or twenty years 
ago for the population of one census to be used year after year 
as the basis of death-rates, or until a new census was taken; 
that is, no intercensal estimates were made. Even the 
registration reports of Massachusetts are full of inconsist- 
encies and cases of disagreements. In the following table 
the general death-rates are given in the second column as 



VARIATION IN DEATH-RATES 



193 




1905 1906 1907 1908 1909 



1910 



1911 



1912 



1913 1914 



Fig. 43. — Comparison of Death-rates in a Large City, a City of 
Moderate Size and a Small Town. 



194 



DEATH-, BIRTH- AND MARRIAGE-RATES 



they appeared originally in successive annual reports. In 
the third column the rates for the same years are given as 
published in the annual report for 1915, the rates having 
been recomputed. 

TABLE 45 
DEATH-RATES IN MASSACHUSETTS 



Year. 


As given 

originally in 

successive 

annual reports. 


As given in 
report of 1915 
(recomputed). 


(1) 


,(2) 


(3) 


1905 
1906 
1907 
1908 
1909 
1910 
1911 
1912 
1913 
1914 


16.8 
16.9 
18.1 
17.2 
17.0 
16.2 
15.8 
15.6 
15.9 
14.5 


16.7 
16.4 
17.2 
16.0 
15.5 
16.1 
15.8 
14.9 
14.9 
14.5 



Rates for short periods. — The general death-rate is 
always computed on the basis of a year. 

Strictly speaking the monthly death-rate would be the 
number of deaths occurring in the month divided by the 
estimated population for the middle of the month; and the 
weekly death-rate would be the number of deaths in a week 
divided by the estimated Wednesday population for that 
week. This practice would reduce population estimates to 
an absurd degree of precision. The months moreover do 
not all have the same number of days. On account of the 
varying estimates of population the sum of the monthly 
rates would not equal the annual rates. 

It is much better for many reasons to reduce all rates 
for short periods to the basis of a year, and to use the popu- 



RELATIONS BETWEEN BIRTH- AND DEATH-RATES 195 

lation estimated for July 1 for all months and weeks of the 
same year. Account must be taken, too, of the varying 
length of the months, and of the fact that a year is not 
exactly fifty-two weeks. 

To find the death-rate for January we therefore multiply 
the number of deaths in January by V/ ? and divide by the 
estimated population for July 1. For the months of thirty 
days the multiplier is \V"j for February it is W" i^ ordi- 
nary years, and V/- in leap years. 

To find the death-rate for any week in the year we mul- 
tiply the number of deaths in the week by -f^ and divide 
by the population estimated for July 1st. 

Birth-rates. — Birth-rates are computed in the same way 
as death-rates. We may have general rates, local rates, 
and resident rates; preliminary rates and final rates; cor- 
rected rates and revised rates. Weekly and monthly rates 
are reduced to a yearly basis. 

One thing should be always remembered. If a child is 
born dead, that is if it is a " still-birth," it is not consid- 
ered by statisticians as a birth. Births include only living 
births. Still-births are placed in a class by themselves. In 
some places, still-births have been included with the living 
births, and in comparing old birth-rates with present rates 
this must be kept in mind. It must be remembered also 
that birth registration is less complete than the registration 
of deaths. 

Relations between birth-rates and death-rates. — The 
relations which exist between general birth-rates and gen- 
eral death-rates are very complicated. It is easy to say that 
because of a naturally high infant mortality, which until 
recently has seldom been less than 10 per cent and which in 
some countries is more than 25 per cent, the birth of many 
children means many deaths and hence a high birbh-rate 
means a high death-rate. To a certain extent this is true. 



196 DEATH-, BIRTH- AND MARRIAGE-RATES 

It is true for a sudden increase in the birth-rate and its 
effect may last for five or ten years if the high birth-rate 
keeps up. But a high birth-rate adds to the population, 
and this increases the denominator of the birth-rate. 
Also most of the babies will within a few years become 
children and enter age groups where the specific death-rates 
are low. If a high birth-rate is long continued it may actually 
reduce the general death-rate. Fifty or sixty years after a 
high birth-rate there should be an excess of persons living 
within the advanced age groups when the specific death- 
rates are high and rapidly increasing. 

Instead of becoming confused by trying to think out 
these puzzling relations, and especially so because wars and 
migrations upset all such reasonings, it is better to regard 
the birth-rate as something which together with deaths and 
migrations controls the age composition of the people. 
Conversely the age composition of the people influences 
both the given birth-rate and the general death-rate. 
One cannot think clearly on this subject without cutting 
loose from general rates and studying specific rates both 
for births and deaths. 

Fecundity. — From a social standpoint the birth-rates 
computed in the usual way give an inadequate idea of some 
of the most important matters concerning the increase of 
population. They are ratios between births and total 
populations, and not all of the population included are 
child producers. If we are to follow the statistical prin- 
ciple of comparing things which are logically comparable 
we shall compute other ratios, that between births and 
women of child bearing age and that between births and 
married women of child bearing age, and we shall separate 
legitimate from illegitmate births, and take into account 
still births, though always keeping them separate from 
living, or true statistical births. 



iJ^ECUNDITY 197 

What are the chief factors which control the number of 
children born? The number of marriages; the effective 
duration of these marriages, that is the number of years be- 
tween the age of the bride at marriage and the natural age 
when child-bearing ceases; and the frequency with which 
conception occurs. The number of marriages depends up- 
on the age and sex composition of the population and upon 
economic and social conditions. The effective duration of 
marriage depends upon the age at marriage, especially 
the age of the bride. Obviously if marriage occurs late in 
life the effective duration of marriage is shortened. The 
frequency of conception depends to some extent upon the 
infant mortality as, a shortening of the period of suckling 
reduces the child-bearing interval; but to a considerable 
extent this is a matter which is, or may be, controlled by 
the husband and wife. The number of still births also has 
an influence on the intervals between living children. 

Korosi ^ and others have attempted to compute tables of 
natality, similar to the life tables described in Chapter XIV. 
Statistics for Budapest indicated that the age of maximum 
fecundity for females reached its maximum between the 
eighteenth and nineteenth years, falling steadily to age 
fifty when it practically ceased. Males attain their maxi- 
mum fecundity at the age of about twenty-five, after which 
there is a steady decline to age sixty-five or thereabouts. 
It is understood that these figures are not physiological 
limits necessarily, but include social and economical con- 
siderations. Late marriages therefore reduce the number 
of resulting children. Combinations of brides and grooms 
of different ages results in different probabilities of births. 
The following figures given by Korosi illustrate this. The 
percentages refer to the probability of a birth occurring in 
a year. 

1 1899, Newsholme, Vital Statistics, p. 667. 



198 DEATH-, BIRTH- AND MARRIAGE-RATE^ 



TABLE 46 
RELATION OF AGE TO FECUNDITY 



Fecundity of mothers. 


Fecundity of fathers. 


Age of 


Age of mother. 


Age of 
mother. 


Age of father. 


father. 


25yrs. 


30 yrs. 


35 yrs. 


25 yrs. 


35 yrs. 


45 yrs. 


55 yrs. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(7) 


(9) 


25-29 


Per 

cent 

36 
31 

27 


Per 
cent 

25 

24 
22 
17 
14 


Per 
cent 
21 
20 
19 
14 
11 
11 


20 
20-24 
25-29 
30-34 
35-39 
40-44 


Per 

cent 

49 
43 
31 
33 


Per 

cent 


Per 

cent 


Per 
cent 


30-34 
35-39 
40-44 
45-49 
50-54 


31 

27 
24 
19 

7 


16 
18 
14 
12 
6 


7 
3 











NationaKties differ considerably in the number of chil- 
dren per marriage. For example, in Russia, the number 
of children per marriage in 1894 averaged as high as 5.7, 
while in France it was only 3.0. During recent years in 
most countries the birth-rates have fallen considerably. In 
studying this subject in its social relations, these natural 
conditions of fecundity as influenced by the age composi- 
tion of the people, the age of marriage and the influence 
of nationahty must be taken into account. 

Illegitimate births. — Children born to unmarried women 
are called illegitimate. In computing general birth-rates 
they are included, but in the study of social problems they 
should be considered by themselves. The illegitimate birth- 
rate is the ratio between illegitimate births and the total 
population expressed in thousands. The percentage of ille- 
gitimacy is sometimes computed, that is the ratio between 
illegitimate and total births, but this ratio may be mislead- 
ing as the total number of births depends on the marriage- 



ILLEGITIMATE BIRTHS 



199 



rate, which fluctuates more or less according to economic 
conditions. As a measure of morality a more useful ratio 
is that between illegitimate births and unmarried women of 
child-bearing age. It is just as important to consider the 
age and sex composition of a population in studying illegiti- 
mate births as in studying all births. 

Newsholme has given the following interesting compari- 
sons between two sections of London, Kensington, an 
aristocratic fashionable district, and Whitechapel, a poor 
industrial parish. 

TABLE 47 
BIRTH-RATES IN KENSINGTON AND WHITECHHAPEL, 1891 



Birth-rate. 


Legitimate. 


Illegitimate. 




Ken- 
sington. 


White- 
chapel. 


Excess 

in 
White- 
chapel. 


Ken- 
sington. 


White- 
chapel. 


Excess 

in 
White- 
chapel. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) ■ 


(7) 


A Per thousand of popula- 
tion 

B Per thousand of women, 
aged 15-44 years 

C Per thousand married 
women, aged 15-44 years 

D Per thousand, unmar- 
ried women, aged 15-44 
years. 


21.8 

61.6 

215.4 


39.9 
172.1 
328.3 


Per 

cent. 

83 

177 

53 


1.2 
3.4 

4.7 


1.3 
5.4 

11.4 


Per 
cent. 

6 

62 

136 











We see from this table that on the basis of married 
women of child-bearing age the birth-rate in the industrial 
district of Whitechapel was only 53 per cent greater than 
in the fashionable district of Kensington. On the basis of 
the general birth-rate or the rate computed for all women 
of child-bearing age the difference between the two districts 



200 DEATH-, BIRTH- AND MARRl AGE-RATES 

would have been said to be much greater. In Kensington 
there were many unmarried servants. The illegitimate 
birth-rate computed on the basis of total population was 
only 6 per cent greater in Whitechapel than in Kensington, 
but on the basis of unmarried women of child-bearing age 
it was 136 per cent greater. This is an excellent example 
of the necessity of considering specific rates in the study 
of illegitimacy. Fallacious conclusions in regard to the 
relative morality of different nationalities, of urban and 
rural districts, of different states and cities have resulted 
from failure to take the proper ratios as a basis of 
study. 

Marriage-rates. — The marriage-rate is found by dividing 
the number of persons married in a year by the estimated 
mid-year population, expressed in thousands. The wed- 
ding-rate would be one-half of the marriage-rate. In some 
places this wedding-rate is called the marriage-rate, but 
this is not according to present-day practice. To prevent 
misunderstanding it is a good plan to use the expression 
" persons married per 1000 population." 

Divorce-rates. — Similarly the divorce-rate is found by 
dividing the number of persons divorced in a year by the 
mid-year population. 

Divorce in the United States is becoming more and more 
important as a social problem. The conditions are dif- 
ferent in different states. In Massachusetts the data, ob- 
tained originally from court records, are published in the 
State Registration Report. The following figures are from 
the report of 1914. 

The divorce-rate, based on an average for five years of 
which the census year was the median, has increased as 
follows. 



DIVORCE-RATES 



201 



TABLE 48 
DIVORCE-RATE, MASSACHUSETTS 



Median 
year. 


Average rate 
per 100,000 
population. 


Average per 
100,000 of mar- 
ried population. 


(1) 


(2) 


(3) 


1880 
1890 
1900 
1905 
1910 
1914 


30 
32 
46 
58 
56 
60 




86 
123 
153 
146 
156 



The relative number of divorces granted to wives is 
larger than the number granted to husbands. At present 
the ratio is in round numbers 7:3. 

The percentage distribution of divorces according to 
cause has been as follows: 

TABLE 49 
CAUSES OF DIVORCE, MASSACHUSETTS, i860 to 1914 



Cause. 



(1) 



Desertion 

Adultery 

Intoxication 

Cruel and abusive treatment 

Nullity of marriage 

Extreme cruelty 

Impotency 

Neglect to provide 

Imprisonment 

Total 



Percentage. 


Granted to 


Granted to 


husband. 


wife. 


(2) 


(3) 


Per cent. 


Per cent. 


56.7 


41.5 


34.8 


• 14.8 


5.8 


14.4 


1.5 


19.8 


0.7 


0.4 


0.2 


4.1 


0.2 


0.2 


1 


4.2 


1 


0.5 



100.0% 



100.0% 



1 Less than 0. 1 per cent. 



202 DEATH-, BIRTH- AND MARRIAGE-RATES 

About three out of every four applications for divorce in 
Massachusetts are granted. About nine out of ten are not 
contested. 

The distribution of divorces according to the duration 
of marriage is interesting. In 1914 the average duration 
of the marriage at the time apphcation for divorce was 
made 10.9 years. The 2963 appHcations were distributed 
as follows: 

TABLE 50 

DURATION OF MARRIAGES ENDING IN DIVORCE 



Duration of 
marriage. 


Per cent of 
applications. 


(1) 


(2) 


0- 6 months 

6-11 

1-4 years 

5-9 '' 
10-19 
20-29 
30 

Total 


0.7 

27.4 
30.7 

28.7 • 
10.3 
2.2 


100.0 



In discussions of the divorce problem comparison is 
sometimes made between marriage-rates and divorce-rates. 
This is not a logical comparison. Why? The student must 
begin to answer such questions as this on the basis of his own 
reasoning. 

In 1910 in Massachusetts divorce was dissolving each year 
about 3 marriages out of every 1000 in existence, or, more* 
exactly, one out of every 342; in 1897 one out of every 
580. 

The U. S. Bureau of the Census has estimated the prob- 
ability of divorce ^ as not less than 1 in 16, and probably 1 
in 12. This figure was based on the statistics of 1900, and 
1 Marriage and Divorce, 1867-1906i Vol. I, pp. 23, 24. 



NATURAL RATE OF INCREASE 



203 



means that one marriage in every 16 would probably be ended 
by divorce instead of continuing until ''death do us part." 

This general figure must not be taken too seriously, as it 
includes all classes of people living under many different con- 
ditions and represents past rather than present conditions. 

Divorce statistics ought to be studied specifically, just as 
much as births and deaths. 

Natural rate of increase. — The difference between the 
birth-rate and the death-rate gives the natural rate of 
increase (or decrease) in population per 1000 inhabitants. 
In the absence of immigration and emigration, and if the 
data are correct, the excess of births over deaths will cor- 
respond with the increase of population as revealed by the 
census counts. This may be illustrated by the statistics of 
Sweden from 1750 to 1900. 



TABLE 51 
INCREASE OF POPULATION IN SWEDEN 







Per 1000 of population at middle of period. 




Population at end 
of given year 
(thousands). 








Year. 


Increase as shown 
by census. 


Excess of births 
over deaths. 


Emigration (com- 
puted from last 
two columns). 


(1) 


(2) 


(3) 


(4) 


(5) 


1750 


1781 


8.89 


8.89 


0.00 


1760 


1925 


7.76 


8.43 


0.67 


1770 


2043 


5.92 


6.60 


0.68 


1780 


2118 


3.71 


4.14 


0.43 


1790 


2188 


3.22 


4.03 


0.81 


1800 


2347 


6.99 


7.96 


0.97 


1810 


2396 


2.04 


2.63 


0.59 


1820 


2584 


7.60 


7.52 


-0.08 


1830 


2888 


11.02 


11.00 


-0.02 


1840 


3139 


8.32 


8.69 


0.37 


1850 


3482 


10.39 


10.51 


0.12 


1860 


3860 


10.36 


11.10 


0.74 


1870 


4169 


7.57 


11.24 


3.67 


1880 


4566 


9.05 


12.21 


3.16 


1890 


4785 


4 69 


12.12 


7.43 


1900 


5136 


7.13 


10.78 


3.65 



204 DEATH-, BIRTH- AND MARRIAGE-RATES 

The figures in the last column show that there was very 
little emigration before 1870, but that since then the losses 
by emigration have been considerable. It is quite likely, 
however, that some of the early birth-rates were not as 
accurate as the more recent ones. 

Comparison of general rates. — The object of computing 
gross death-rates is to enable us to compare the general 
mortality in places of different population and of different 
years in the same place; and yet, as will be demonstrated in 
the .next chapter, such comparisons are very apt to be mis- 
leading unless the percentage composition of the popu- 
lation remains substantially constant in all the places and 
in all the years which are compared. One naturally asks, 
" Why, if such is the case, should we compute it at all? '' 
The answer is that in a general and crude way the gross 
rate does show differences in the mortality of different 
places, and that in any given place the composition of the 
population changes slowly from year to year. Large differ- 
ences in general death-rates may be significant, but small 
differences are usually not significant. 

What is true of general death-rates is also true of birth- 
rates and marriage-rates. Far too much attention in 
studies of vital statistics is given to comparisons of general 
rates. Such comparisons are likely to be superficial and 
sterile of results. Nevertheless one should have a general 
appreciation of the changes which have taken place in 
birth-rates and death-rates throughout the world during 
the last fifty years. A few examples will be given, but 
the reader should consult more extended works on the 
subject and compile for himself tables of rates taken from 
official reports. 

Marriage-rates, birth-rates and death-rates in Sweden. 
— One of the longest records of birth-rates, marriage-rates 
and death-rates is that of Sweden. Table 48 shows these 



VITAL STATISTICS OF SWEDEN 



205 




0061 



068T 



088T 



0Z8T 



0981 



0S81 



W8T 



0881 



0T8T 



0081 



06X1 



mil 



our 



09£t 



osu 



206 DEATH-, BIRTH- AND MARRIAGE-RATES 

rates from 1749 to 1900. The death-rates and birth-rates 
are also shown in Fig. 44. It will be seen that the birth- 
rate has had a general downward trend for a long time, but 
especially during the last fifty years. The death-rate has 
fallen more than the birth-rate so that the natural in- 
crease has risen. Of course, there have been fluctuations 
and some very abnormal rates will be found. As one would 
naturally expect the birth-rate has fluctuated synchro- 
nously with the marriage-rate. At intervals great epi- 
demics have occurred which carried the death-rate far above 
the birth-rate. As a statistical series this diagram is de- 
serving of careful study. The dotted line shows the " mov- 
ing average " referred to in Chapter II. 



MARRIAGE-, BIRTH- AND DEATH-RATES, SWEDEN 207 



TABLE 48 

MARRIAGE-RATES, BIRTH-RATES, AND DEATH-RATES 

Sweden, 1749- 1900 (After Sundbarg) 



Year. 


Mar- 
riage- 
rate. 


Birth- 
rate. 


Death- 
rate. 


Natural 

in- 
crease. 


Year. 


Mar- 
riage- 
rate. 


Birth- 
rate. 


Death- 
rate. 


Natural 
increase. 


(1) 


(2) 


(3) 


(4) 


(5) 


(1) 


(2) 


(3) 


(4) 


(5) 


1749 


17.10 


33.82 


28.13 


5.69 












1750 


18.48 


36.40 


28.83 


9.57 


1780 


17.06 


35.70 


21.74 


13.96 


1751 


18.54 


38.63 


26.18 


12.45 


1781 


14.66 


33.46 


25.55 


7.91 


1752 


18.52 


35.91 


27.34 


8.57 


1782 


15.36 


32.05 


27.26 


4.79 


1753 


17.42 


36.12 


24.03 


12.09 


1783 


15.98 


30.33 


28.11 


2.22 


1754 


18.90 


37.22 


26.33 


10.89 


1784 


14.96 


31.53 


29.75 


1.78 


1755 


18.32 


37.52 


27.38 


10.14 


1785 


15.64 


31.43 


28.30 


3.13 


1756 


17.00 


36.12 


27.66 


8.46 


1786 


16.04 


32.89 


25.94 


6.95 


1757 


15.94 


32.61 


29.92 


2.69 


1787 


15.90 


31.47 


23.95 


7.52 


1758 


16.14 


33.42 


32.37 


1.05 


1788 


15.78 


33.87 


26.68 


7.19 


1759 


19.50 


33.62 


26.27 


7.35 


1789 


15.86 


32.01 


33.13 


-1.12 


1760 


19.52 


35.70 


24.78 


10.92 


1790 


16.50 


30.48 


30.43 


0.05 


1761 


18.88 


34.82 


25.80 


9.02 


1791 


21.68 


32.63 


25.49 


7.14 


1762 


17.92 


35.08 


31.22 


3.86 


1792 


20.02 


36.58 


23.90 


12.68 


1763 


17.28 


34.98 


32.90 


2.08 


1793 


17.80 


34.39 


24.27 


10.12 


1764 


17.58 


34.70 


27.24 


7.46 


1794 


16.36 


33.79 


23.60 


10.19 


1765 


16.30 


33.41 


27.68 


5.73 


1795 


15.18 


32.04 


27.94 


4.10 


1766 


16.54 


35.36 


25.06 


10.30 


1796 


17.24 


34.68 


24.65 


10.03 


1767 


16.54 


35.36 


25.63 


9.73 


1797 


16.88 


34.77 


23.81 


10.96 


1768 


16.92 


33.61 


27.17 


6.44 


1798 


16.58 


33.68 


23.08 


10.60 


1769 


16.26 


33.06 


27.15 


5.91 


1799 


14.70 


32.02 


25.18 


6.84 


1770 


16.24 


32.98 


26.06 


6.92 


1800 


14.90 


28.72 


31.43 


0.9 


1771 


15.52 


32.24 


27.77 


4.47 


1801 


14.50 


30.04 


26.08 


3.96 


1772 


13.64 


28.89 


37.41 


-8.52 


1802 


15.66 


31.72 


23.71 


8.01 


1773 


15.52 


25.52 


52.45 


-26.93 


1803 


16.38 


31.36 


23.77 


7.59 


1774 


8.77 


34.45 


22.36 


12.09 


1804 


16.14 


31.90 


24.87 


7.03 


1775 


18.90 


35.63 


24.84 


10.79 


1805 


16.74 


31.73 


23.48 


8.25 


1776 


18.02 


32.92 


22.50 


10.42 


1806 


16.08 


30.75 


27.51 


3.24 


1777 


18.14 


33.03 


24.93 


8.12 


1807 


16.40 


31.16 


26.22 


5.94 


1778 


18.10 


34.82 


26.65 


8.17 


1808 


16.24 


30.39 


34.85 


5.54 


1779 


17.34 


36.70 


28.50 


8.20 


1809 


15.62 


26.67 


40.04 


13.37 



DEATH-, BIRTH- AND MARRIAGE-RATES 



TABLE 48 

MARRIAGE-RATES, BIRTH-RATES, AND DEATH-RATES 

Sweden, 1749- 1900 (After Simdbarg) 



Year. 


Mar- 
riage- 
rate. 


Birth- 
rate. 


Death- 
rate. 


Natural 

in- 
crease. 


Year. 


Mar- 
riage- 
rate. 


Birth- 
rate. 


Death- 
rate. 


Natural 
increase. 


(1) 


(2) 


(3) 


(4) 


(5) 


(1) 


(2) 


(3) 


(4) 


(5) 


1810 


21.52 


32.95 


31.57 


1.38 


1840 


14.14 


31.43 


20.35 


11.08 


1811 


21.32 


35.30 


28.81 


6.49 


1841 


14.34 


30.33 


19.42 


10.91 


1812 


18.26 


33.57 


30.27 


3.30 


1842 


14.22 


31.65 


21.06 


10.59 


1813 


15.48 


29.74 


27.37 


2.37 


1843 


14.38 


30.78 


21.45 


9.33 


1814 


15.04 


31.19 


25.07 


6.12 


1844 


14.88 


32.15 


20.27 


11.88 


1815 


19.22 


34.77 


23.59 


11.18 


1845 


14.58 


31.45 


18.83 


12.62 


1816 


19.60 


35.32 


22.66 


12.66 


1846 


13.80 


29.94 


21.83 


8.11 


1817 


16.68 


33.40 


24.25 


9.15 


1847 


13.64 


29.58 


23.69 


5.89 


1818 


16.92 


33.83 


24.37 


9.46 


1848 


14.64 


30.33 


19.68 


10.65 


1819 


16.28 


32.99 


27.36 


5.63 


1849 


15.66 


32.84 


19.84 


13.00 


1820 


16.88 


32.97 


24.46 


8.51 


1850 


15.18 


31.89 


19.79 


12.10 


1821 


17.62 


35.44 


25.57 


9.87 


1851 


14.72 


31.74 


20.72 


11.02 


1822 


18.58 


35.88 


22.59 


13.29 


1852 


13.68 


30.69 


22.70 


7.99 


1823 


17.98 


36.83 


21.02 


15.81 


1853 


14.40 


31.37 


23.66 


7.71 


1824 


17.66 


34.56 


20.77 


13.79 


1854 


15.38 


33.50 


19.76 


13 74 


1825 


17.20 


36.49 


20.54 


15.95 


1855 


15.04 


31.75 


21.45 


10.30 


1826 


16.16 


34.84 


22.61 


12.23 


1856 


14.88 


31.47 


21.77 


9.70 


1827 


14.44 


31.30 


23.05 


8.25 


1857 


15.50 


32.43 


27.58 


4.85 


1828 


15.82 


33.61 


26.74 


6.87 


1858 


16.22 


34.77 


21.69 


13.08 


1829 


15.82 


34.85 


28.97 


5.88 


1859 


16.56 


34.99 


20.13 


14.86 


1830 


15.46 


32.91 


24.08 


8.83 


1860 


15.60 


34.83 


17.65 


17.18 


1831 


13.80 


30.49 


26.00 


4.49 


1861 


14.54 


32.57 


18.47 


14.10 


1832 


14.38 


30.86 


23.38 


7.48 


1862 


14.52 


33.38 


21.40 


11.98 


1833 


15.66 


34.11 


21.74 


12.37 


1863 


14.52 


33.62 


19.33 


14.29 


1834 


16.02 


33.74 


25.68 


8.06 


1864 


13.96 


33.61 


20.25 


13.36 


1835 


15.00 


32.67 


18.55 


14.12 


1865 


14.14 


32.81 


19.36 


13.45 


1836 


14.34 


31.84 


19.97 


11.87 


1866 


13.44 


33.11 


19.98 


13.13 


1837 


13.80 


30.84 


24.65 


6.19 


1867 


12.18 


30.83 


19.64 


11.19 


1838 


12.18 


29.37 


24.10 


5.27 


1868 


10.92 


27.47 


20.98 


6.49 


1839 


13.54 


29.49 


23.56 


5.93 


1869 


11.28 


28.25 


22.27 


5.98 



MARRIAGE-, BIRTH- AND DEATH-RATES, SWEDEN 209 



TABLE 48 

MARRIAGE-RATES, BIRTH-RATES, AND DEATH-RATES 

Sweden, 1749- 1900 (After Sundbarg) 



Year. 


Mar- 
riage- 
rate. 


Birth- 
rate. 


Death- 
rate. 


Natural 

in- 
crease. 


Year. 


Mar- 
riage 
rate. 


Birth- 
rate. 


Death- 
rate. 


Natural 
increase. 


(1) 


(2) 


(3) 


(3) 


(5) 


(1) 


(2) 


(3) 


(4) 


(5) 


1870 


12.04 


28.78 


19.80 


8.98 












1871 


12.98 


30.42 


17.21 


13.21 












1872 


13.86 


30.04 


16.28 


13.76 












1873 


14.62 


30.80 


17.20 


13.60 












1874 


14.54 


30.85 


20.32 


10.53 












1875 


14.10 


31.17 


20.27 


10.90 












1876 


14.16 


30.84 


19.59 


11.25 












1877 


13.66 


31.07 


18.66 


12.41 












1878 


12.94 


29.83 


18.06 


11.77 












1879 


12.58 


30.52 


16.94 


13.58 












1880 


12.64 


29.36 


18.10 


11.26 












1881 


12.38 


29.07 


17.68 


11.39 












1882 


12.66 


29.35 


17.35 


12.00 












1883 


12.86 


28.94 


17.31 


11.63 












1884 


12.06 


30.01 


17.53 


12.48 












1885 


13.26 


29.44 


17.75 


11.69 












1886 


12.82 


29.76 


16.61 


13.15 












1887 


12.50 


29.66 


16.13 


13.53 












1888 


11.84 


28.78 


15.99 


12.79 












1889 


11.98 


27.74 


15.99 


11.75 












1890 


11.98 


27.95 


17.12 


10.83 












1891 


11.66 


28.27 


16.81 


11.46 












1892 


11.38 


26.98 


17.88 


9.10 












1893 


11.30 


27.36 


16.83 


10.53 












1894 


11.48 


27.10 


16.38 


10.72 












1895 


11.74 


27.49 


15.19 


12.30 












1896 


11.90 


27.18 


15.64 


11.54 












1897 


12.12 


26.67 


15.35 


11.32 












1898 


12.28 


27.11 


15.08 


12.03 












1899 


12.48 


26.35 


17.65 


8.70 












1900 


12.30 


27.00 


16.84 


10.16 













210 DEATH-, BIRTH- AND MARRIAGE-RATES 



Downward trend in birth-rates and death-rates. — 

For nearly half a century there has been a general down- 
ward trend in the birth-rates and death-rates of almost all 
civilized countries. There is space here for only a few 
figures which represent averages for quinquennial periods. 
They are taken from the reports of the Registrar-General 

of England. 

TABLE 49 

CHRONOLOGICAL CHANGES IN VITAL RATES 



Country. 


Quinquennial averages. 




1881-5 


1886-90 


1891-5 


1896-00 


1901-5 


1906-10 


1911-15 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 



Birth-rates. 



England and Wales 
Germany 
France 
Hungary 



33.5 


31.4 


30.5 


29.3 


28.1 


26.3 


37.0 


36.5 


36.3 


36.0 


34.3 


32.7 


24.7 


23.1 


22.3 


21.9 


21.2 


19.9 


44.6 


43.7 


41.7 


39.4 


37.2 


37.0 



23.6 



Death-rates. 



England and Wales 


19.4 


18.9 


18.7 


17.7 


16.0 


14.7 


14.3 


Germany 


25.3 


24.4 


23.3 


21.2 


19.9 


17.5 




France 


22.2 


22.0 


22.3 


20.7 


19.6 


19.2 


.... 


Hungary 


33.1 


32.1 


31.8 


27.9 


26.2 


25.0 


.... 



Rates of natural increase. 



England and Wales 
Germany 
France 
Hungary 



14.1 

11.7 

2.5 

11.5 



12.5 

12.1 

1.1 

11.6 



11.8 

13.0 

0.0 

9.9 



11.6 

14.8 

1.2 

11.5 



12.1 

14.4 

1.6 

11.0 



11.6 

15.2 

0.7 

12.0 



9.3 



In most countries the natural rate of increase tends to 
lie between the limits of 8 and 14 per 1000, i.e., between 
0.8 and 1.4 per cent, but sometimes it runs above 1.4 per 
cent or below 0.8 per cent per year. France is an example of 



VARIATIONS DUE TO POPULATION ESTIMATES 211 



an extremely low rate of natural increase. In Germany both 
the birth-rates and death-rates have be^n higher than in 
England. In Hungary both rates have been much higher 
than in Germany, yet the rate of natural increase has been 
lower. The student should seek to explain all of these facts. 



,3,400,000 

3,200,000| 
a 

"3 
,000,000 ;2 

2,800,000 

1910 
^3,400,000 

3,200,000 § 




i 
«17 

a 
o 



15 



'-'^ 






A 


7 








L: 


--7 






f 


B 




\_5f 








1 




1 



3 

'3,000,000 1" 



2,800,000 



1900 1905 1910 

Fig. 45. — Estimated Death-rates and Populations, Massachu- 
setts, 1900-1910. 

Variations due to population estimates. — Some of the 
variations in the general death-rates from year to year are 
due to the use of incorrect population estimates. The 
following comparison is interesting. 

Fig. 45 shows the populations and death-rates for the state 
of Massachusetts from 1900 to 1910, based on the following 
data : ^ 

^ Registration Report, 1914, p. 176. 



212 



DEATH-, BIRTH- AND MARRIAGE-RATES 



TABLE 50 
DEATH-RATES: MASSACHUSETTS 



Year. 


Population. 


Deaths. 


Death-rates. 


(1) 


(2) 


(3) 


(4) 


1900 


2,805,346 (census) 


51,156 


18.2 


1901 


2,849,047 


48,275 


16.9 


1902 


2,889,386 


47,491 


16.4 


1903 


2,929,725 


49,054 


16.7 


1904 


2,970,064 


48,482 


16.3 


1905 


3,015,872 (census) 


50,486 


16.7 


1906 


3,089,029 


50,624 


16.4 


1907 


3,162,186 


54,234 


17.2 


1908 


3,235,343 


51,788 


16.0 


1909 


3,308,500 


51,236 


15.5 


1910 


3,380,151 (census) 


54,407 


16.1 



The upper diagram shows the estimated population as 
a uniform change from 1900 to 1905 and again from 1905 to 
1910. The death-rates computed from the actual deaths 
and estimated populations are seen to vary irregularly. 
But suppose we assume that the changes in death-rates 
between 1900 and 1905 and 1905 and 1910 are uniform. 
Then we can compute the changes in population from 
these estimated rates and the actual deaths. The results 
are shown in the lower diagram. Do these irregular fluc- 
tuations seem to be reasonable? 

There is no way of telling exactly how much of the in- 
crease or decrease in the general death-rate is due to actual 
increase in mortality and how much to error in the esti-j 
mated population. Both factors are involved. 

Birth-rates and death-rates in Massachusetts. — Fig. 
46 shows the annual variations in birth-rates and death- 
rates from 1850 to 1915. The stars indicate the so-called 
panic years, or years of business depression. The tendency 
has been for the marriage-rate and the birth-rate to fall 
for a number of years after a period of depression. Since 



BIRTH- AND DEATH-RATKS IN MAS8ACHUSETTIS 213 



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214 DEATH-, BIRTH- AND MARRIAGE-RATES 

1892 the death-rate has decreased considerably. The 
general synchronism between the birth-rate and the death- 
rate should be noticed, — and also the numerous excep- 
tions to the rule. 

In recent years there has been a marked tendency towards 
uniformity in the death-rate, not only in the state as a 
whole from year to year, but among the subdivisions of 
the state in any given year. 

The fluctuations from year to year are due in part to 
incorrect estimates of population. 

Monthly death-rates in Massachusetts. — The general 
death-rate is not constant throughout the year, but varies 
seasonally. There are several ways in which this may be 
shown. The following figures are for the state of Massa- 
chusetts for the year 1915. 



TABLE 51 
MONTHLY DEATH-RATES: MASSACHUSETTS, 1915 



Month. 


Rate. 


Per cent of 
annual rate. 


(1) 


(2) 


(3) 


Jan. 
Feb. 
Mar. 

Apr. 
May • 
June 

July 
Aug. 
Sept. 

Oct. 

Nov. 

Dec. 

Year 


14.65 
13.60 
16.80 

17.45 
13.95 
12.35 

12.55 
13.10 
13.75 

13.40 
13.10 
16.00 

14.40 


102 

C4 

117 

121 
97 
86 

87 
91 
96 

93 

91 

111 

100 



MARRIAGE-RATES IN MASSACHUSETTS 215 

Monthly rates vary considerably from year to year in 
the same place and are different for different places. 
Climatic conditions have an influence on these short term 
rates. The chance occurrence of communicable diseases 
also has its effect. Weekly rates fluctuate even more 
widely than monthly rates, and daily rates a fortiori. 

The ten year average for Massachusetts for 1905-14 gave 
the highest winter rate for February and not for April as 
in 1915; and the highest summer rate was in August, not 
September as in 1915. 

The student should compute and study monthly rates 
for places where the climatic conditions are different. 

Marriage-rates in Massachusetts. — Marriage-rates rise 
and fall periodically. The rate is influenced by social and 
economic conditions, by the age distribution of the popu- 
lation, the ratio of the sexes at marriageable age, by nation- 
ality, and by many causes. There has been no steady 
downward trend in the marriage-rate as in the case of the 
death-rate and birth-rate. There is, however, a seasonal 
variation. June and October are the most popular months 
for weddings. 

In 1915 the Massachusetts marriage-rate for the year was 
17.0; in June it was 27.5, in October, 23.9, but in March 
only 6.6. There were four times as many weddings in June 
as in March. 

Since 1870 the median marriage-rate in Massachusetts 
has been 18.0. After the panic of 1873 the annual rates for 
several years ranged between 15 and 16.5, and after other 
periods of business depression they have been below 17. 
The highest annual rate in nearly fifty years was during 
1871 and 1872, when it was 21.1 per thousand. 

The published statistics of marriages generally include 
tables classified according to the age and nativity of the 
bride and groom ; the number of the marriage (whether first, 



216 DEATH-, BIRTH- AND MARRIAGE-RATES 

second, third, etc.); and the previous state of the persons 
wed (whether bachelors, maids, widowers, or widows). 

Divorce-rate in Massachusetts. — In 1915 the number 
of persons divorced was 1.22 per 1000 population; in 1914 
the rate was 1.21; in 1910, 1.15; in 1890, 0.58; in 1870, 
0.52. 

Limited use of general death-rates (gross rates). — 
General death-rates are composite figures. They cover 
the entire population, both sexes, all ages and nationali- 
ties, all occupations, all causes of death, while the estimates 
of population are often inaccurate. Fluctuations from year 
to year depend in part on the size of the population, in part 
upon the composition of the population, as well as upon 
causes of death. Under these conditions it is evident that 
they cannot be safely used as an index of mortality condi- 
tions in different places and for long periods of time in any 
one place. 

A general death-rate, or gross death-rate, is of little use 
until it has been analyzed. 

The ^Hotal solids" in a water analysis gives the chemist 
almost no idea of the quality of the water: it is necessary to 
separate the " solids " into their constituent parts. In the 
same way a general death-rate must be broken up into its 
constituent parts. At the present time the analysis of 
death-rates is practiced but little. Death-rate analysis 
today is in about the same condition that water analysis 
was in fifty years ago. 

The necessary analysis cannot be made until the im* 
portant subject of specific death-rates has been considered 
in the next chapter. 

The ideal death-rate. — Is there such a thing as an ideal 
death-rate? At present our general death-rates are falling. 
They cannot continue to fall forever, for man is mortal 
and all must die? A large part of the decrease in the 



THE IDEAL DEATH-RATE 217 

death-rate can be traced to sanitary, hygienic and medical 
improvements. Another part may be due to a lowering 
birth-rate following a relatively high birth-rate, or in other 
words to an increasing ratio of persons in the young and 
middle-aged groups. This condition will not continue 
permanently. In due course the young will become middle 
aged and the middle aged will become old, the excess of 
population will enter those age-groups where the specific 
death-rates are high and this will cause the general death- 
rate to rise. Or the birth-rate will rise and temporarily 
this will raise the general death-rate. 

Unless public health officials learn how to view general 
death-rates in a proper light — a good way being not to 
view them at all — they may be surprised and discouraged 
some day to find that the death-rate is rising. 

The Great War in a most horrible and pitiful way cut 
out a large number of males in the middle-aged groups in 
many countries. Temporarily this will increase the gen- 
eral death-rate. On the other hand these young men will 
not live to enter the old-age groups where the specific 
death-rates are high. What effect will this have on the 
future trend of the death-rate? What effect will it have on 
the birth-rate? 

Perhaps it may be for the best interest of the race that 
the general death-rate be higher than it now is. This 
would be the case if there should be more babies and more 
grandfathers and grandmothers. • To answer the ques- 
tion as to what is the lowest practicable death-rate we 
must first decide what is an ideal distribution of popula- 
tion as to age and sex, and then consider what diseases at 
the different ages we can reasonably expect to eliminate. 
It is an interesting problem for thought and discussion. 



218 DEATH-, BIRTH- AND MARRIAGE-RATES 



EXERCISES AND QUESTIONS 

1. Plot the general death-rates of Massachusetts by years from 1850 
to date. Connect the points with straight lines. Then draw straight 
lines connecting the death-rates for the years divisible by ten. Why is 
the resulting curve so regular? Connect the points for years ending in 
9. Why is the resulting curve so irregular? 

2. Compare the published statistics for tuberculosis as given by 
local, state and federal authorities. Explain the differences. [See Am. 
J. P. H., May 1913, p. 431.] 

3. Compute the following death-rates, carrjdng the results only as 
far as accuracy warrants. 



Population 


Deaths per year 


5,461,200 


70,210 


261,500 


2,913 


35,000 


421 


5,260 


98 


897 


17 



4. How does the marriage-rate ordinarily compare with the ratio of 
marriages to persons eligible to marriage (bachelors, spinsters, widowers, 
widows and divorced persons, all of marriageable age)? [Newsholme's 
"Vital Statistics," p. 58.] 

5. How do the marriage-rates in cities compare with those in rural 
districts? 

6. Is the marriage-rate a reliable "barometer of prosperity," as Dr. 
Farr called it? 

7. What effect has war on the marriage-rate? 

8. What proportion of marriages are remarriages? 

9. Are remarriages more common among widowers or widows? 

10. Prepare a table showing the marriage state (single, married, 
widowed, divorced) of the population of some civil division for each 
sex and for different age-groups above age fifteen. [Consult census 
reports.] 

11. At what ages do people in different social positions marry? 



EXERCISES AND QUESTIONS 219 

12. What changes, if any, have taken place in the age of marriage 
among people of different social position during recent years? 

13. How do the general birth-rates for urban and rural districts 
compare with each other? 

14. How do the birth-rates for urban and rural districts compare 
with each other if based on the number of married women of child- 
bearing age? 

15. What relation is there between birth-rates based on married 
women of child-bearing age and the social position of these women? 

16. What relation is there between the birth-rate thus computed 
and the age of marriage? 

17. What influence has war on the general birth-rate? 

18. What influence has national prosperity on fecundity? 

19. How do the general birth-rates compare for different political 
countries, such as England, Ireland, France, Germany, Austria, Bel- 
gium, etc. 

20. How do the birth-rates for different nationalities in the United 
States compare with each other? 

21. How does the birth-rate for the Irish in Ireland compare with 
that of the Irish in Massachusetts? 

22. How do the birth-rates among Cathohcs compare \vith that 
among Protestants? Consult the statistics of Canada, especially the 
provinces of Ontario and Quebec. 

23. What is the ratio of males to females among births? 

24. What is the ratio of males to females among still-births? 

25. What is the ratio of males to females among illegitimate 'births? 



CHAPTER VII 
SPECIFIC DEATH-RATES 

Although general death-rates have their uses, something 
more is needed if statistics of mortality are to be used 
to their best advantage. The tendencies of human beings 
to die are not constant; diseases differ] in their fatality; 
persons of different age differ in susceptibility to disease; 
sex, nationality, connubial condition are likewise variable 
factors. One cannot properly use mortality statistics in 
public health work without taking these factors into ac- 
count, at least without considering the most important of 
them. This brings us to a consideration of specific death- 
rates. ^General death-rates are ratios between the entire 
population of a given place and all deaths which occur in 
a year. u' We may restrict these rates in several ways. 

Restrictions of death-rates. — We may consider a 
shorter period than a year, and compute the rate for a month 
or a week and thus obtain a partial rate or a short-term 
rate as described in the previous chapter. This, however, 
is not usually classed as a specific rate. 

We may restrict the computation to a special class or 
group of the population; that is, we may take into account 
only males or only females and compute the death-rate 
for them alone. These would be specific death-rates by 
sex. We may consider each age-group by itself and find 
the death-rate for it alone. This would be to compute 
specific death-rates by age-groups. Or we may take only 
persons of the same nationality or occupation and com- 
pute specific death-rates for them. 

220 



AGE 221 

• 

Again we may consider separately the different causes of 
death, and compute specific death-rates for tuberculosis, 
for scarlet fever, or for cancer. 

Finally we may consider particular diseases and at the 
same time restrict the computation to certain classes or 
groups of people; thus we may compute the '^ typhoid 
fever death-rate for males in age group 15-19 years." 

It has been suggested that these various modes of re- 
striction might be designated by such expressions as 
''special death-rates," ''particular" rates, "limited" rates, 
etc., but apparently the common expression " specific " 
death-rate serves every useful purpose. 

It is the purpose of the present chapter to describe the 
methods of computing specific rates and to call attention 
to their importance. It is not too much to say that an 
understanding of specific rates is the key to the interpretation 
of vital statistics. Failure to appreciate the important influ- 
ences of age is alone responsible for scores of fallacious 
conclusions derived from tables of vital statistics. 

Age. — The span of human life has been divided into age 
periods in many different ways. Shakespeare^ vividly 
describes the seven ages of man. 

Jagues: All the world's a stage, 
And all the men and women merely players: 
They have their exits and their entrances; 
And each man in his time plays many parts, 
His acts being seven ages. At first the infant, 
Mewling and puking in the nurse's arms; 
Then the whining school-boy, with his satchel 
And shining morning face, creeping like snail 
Unwillingly to school; and then the lover, 
Sighing like furnace, with a woeful ballad 
Made to his mistress' eyebrow; then a soldier. 
Full of strange oaths and bearded like the pard, 

1 Jaques in As You Like It, Act II, Scene VII. 



222 SPECIFIC DEATH-RATES 

Jealous in honour, sudden and quick in quarrel, 

Seeking the bubble reputation 

Even in the cannon's mouth; and then the justice, 

In fair round belly with good capon lin'd, 

With eyes severe and beard of formal cut, 

Full of wise saws and modern instances; 

And so he plays his part; the sixth age shifts 

Into the lean and slipper 'd pantaloon, 

With spectacles on nose and pouch on side, 

His youthful hose well sav'd, a world too wide 

For his shrunk shank; and his big manly voice. 

Turning again toward childish treble, pipes 

And whistles in his sound; last scene of all, 

That ends this strange eventful history, 

Is second childishness and mere oblivion, 

Sans teeth, sans eyes, sans taste, sans every thing. 

Just where to draw the age hnes between Shakespeare's 
seven ages is a most difficult matter and it would be hard 
to get any two people to agree. The divisions suggested in 
Fig. 47 are merely for provoking discussion. 

Physiologically seven fairly distinct states may be recog- 
nized — the pre-natal state, infancy, childhood, youth 
(maidenhood), early manhood and manhood (child-bear- 
ing age and maturity), and finally old age, or senility. 
The age limits of the early groups are fairly well marked. 
The. later groups are more indistinct. He would be a bold 
person who would undertake to establish an age limit for 
senility. Every one knows what was said about Dr. 
Osier when he attempted to do something of that sort. In 
Fig. 47 the biblical limit of ^^ three score years and ten " 
has been used. The author believes that he may safely 
hide behind that. The division between childhood and 
youth in boys is perhaps not quite the same as the division 
between childhood and maidenhood in girls. 

From the standpoint of environment there are several 
fairly distinct age periods. Infancy in this case means the 



AGES OF MAN 



223 



Envlroment 



Physiological State 



Shakespeares 

Seven Ages 

of Man 



Occurence of 

Diseases 1 i> 

Per cent per year 
(After Pearson) 



Specific death, rate, 
according to age. 




10 20 30 40 50 60 

Fig. 47. — Ages of Man. 



224 SPECIFIC DEATH-RATES 

earliest period, in which the environment is maternal. It 
terminates when the child is weaned. Then follows the 
period of home environment. Later the school environ- 
ment controls. After that the work place comes in as an 
important factor. Of course the home influence continues 
through life, and in the case of most women it predominates 
after the school age. Indeed after the school age the 
environment becomes complex. 

Karl Pearson has analyzed the curve which shows the 
age distribution of deaths in an interesting way. He con- 
cludes that there are five groups of diseases, those of in- 
fancy, childhood, youth, middle age and old age. All of 
these extend over wide limits, but culminate at the ages 
shown in Fig. 47. One may die of an old age disease at 
thirty, or one may have a children's disease at forty. 
Endless complications exist in special cases, yet in the main 
the distinctions between the five classes of diseases are well 
known. 

At the bottom of the diagram we see the curve which 
shows the specific death-rate in its characteristic variations 
through the span of life. This curve in its general form is 
the same for both sexes, for all nationalities, for all climates. 
There are differences, of course, but over all the other 
factors which influence death, age predominates. This 
curve, it should be observed, is based on deaths from all 
causes. It would not necessarily apply to particular diseases. 

The student should study this curve of specific death- 
rates according to age until he can reproduce it with ap- 
proxim^ate accuracy from memory. 

Vision of Mirza. — Those who do not enjoy studying 
statistics may appreciate the following paragraph taken 
from Addison's '' Vision of Mirza." 

'^ The bridge thou seest, said he, is Human Life; con- 
sider it attentively. Upon a more leisurely survey of it, 



HOW TO COMPUTE SPECIFIC DEATH-RATES 225 

I found that it consisted of threescore and ten entire arches, 
with several broken arches, which, added to those that were 
entire, made up the number about an hundred. As I was 
counting the arches, the Genius told me that this bridge 
consisted at first of a thousand arches; but that a great flood 
swept away the rest, and left the bridge in the ruinous con- 
dition I now beheld it. But tell me further, said he, 
what thou disco verest on it. I see multitudes of people 
passing over it, said I, and a black cloud hanging on each 
end of it. As I looked more attentively, I saw several of 
the passengers dropping through the bridge into the great 
tide that flowed underneath it: and upon further exami- 
nation perceived that there were innumerable trap-doors 
that lay concealed in the bridge which the passengers no 
sooner trod upon, but they fell through them into the tide, 
and immediately disappeared. These hidden* pit-falls 
were set very thick at the entrance of the bridge, so that 
throngs of people no -sooner break through the cloud, but 
many of them fell into them. They grew thinner towards 
the middle, but multiplied and laid closer together towards 
the end of the arches that were entire. There were, in- 
deed, persons, but their number was very small, that con- 
tinued a kind of hobbling march of the broken arches, but 
fell through one after another, being quite tired and spent 
with so long a walk." 

How to compute specific death-rates. — The specific 
death-rate for any age-group is found by dividing the 
number of deaths of persons whose ages lie within the 
group limits by the number of thousands of persons in 
the same group alive at mid-year. The computation is pre- 
cisely the same as that for the general death-rate except 
that both deaths and population are confined to specific 
age-groups, u If both quantities are known the process is 
merely arithmetical. 



226 



SPECIFIC DEATH-RATES 



Example: — Given the following data for New South 
Wales, 1901 (Columns 1, 2, 3). 



TABLE 52 



Age-group. 


Population. 


Deaths. 


Specific death- 
rate. 


(1) 


(2) 


(3) 


(4) 


0-1 

1-19 
20-39 
40-59 
60- 

Total 


40,500 

704,000 

514,900 

256,600 

89,800 

1,605,800 


3,234 
1,960 
2,251 
2,965 
5,400 
15,810 


79.9 

2.8 

4.4 

11.6 

60.1 

9.85 



To find the specific death-rate for the age-group 1-19 
years,- dit'ide the number of deaths in that group, i.e., 1960 
by 704, the number of thousands of population. The result 
is 2.8 per 1000. Similarly the specific death-rate for age- 
group 20-39 is 2251 -- 515 = 4.4 per 1000. The figures 
in Column 4 were thus computed. The total deaths di- 
vided by the total population, in thousands, gives the gen- 
eral death-rate, i.e., 15810 ^ 1605.8 = 9.85 per 1000. 

If the number of deaths within the age-group is known 
but the population is unknown, it is necessary to estimate 
the population in the group. This can usually be done with 
sufficient accuracy from the data provided by the censuses. 
The methods of making these estimates both for censal and 
non-censal years has been already described. This may* 
involve a redistribution of the population from those given 
in the census to those corresponding to the death statistics. 

If the population in the group is known but the number 
of deaths is unknown the computation cannot be made with 
accuracy. It might be possible to redistribute the deaths 
into age-groups corresponding to the population, but 



DEATH-RATES BY AGES FOR MALES AND FEMALES 227 
240r 

220 

200 

180 



160 



140 



§,120 
100 



80 



60 



40 



20 

















1 




























































/ 








SPECIFIC DEATH RATES 

OF 

MALES AND FEMALES 

IN 

ORIGINAL REGISTRATION STATES 

1910 

FROM U.S. LIFE TABLES PREPARED 

BY PROF. JAMES. W. GLOVER, FOR 

THE BUREAU OF THE CENSUS, 1916 














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10 



20 



30 



40 50 60 

Age in Years 



70 



80 



90 



100 



Fig. 48. — Specific Death-rates. i 

specific death-rates obtained in this way would in most 
cases be unrehable. 

Specific death-rates by ages for males and females. — 
Looking at the two curves for the specific death-rates of 
males and females shown in Fig. 48 one would say at -first 
that they were much alike, but that the rates at all ages were 



228 



SPECIFIC DEATH-RATES 



higher for males than for females. In a general way this is 
true, but a closer study shows that the differences are not 
the same for all ages. The table from which these curves 
were plotted gave data from which the following figures 
were obtained. 

TABLE 53 

PER CENT BY WHICH THE SPECIFIC DEATH-RATES FOR 
MALES EXCEEDED THOSE FOR FEMALES IN VARIOUS 
AGE INTERVALS 

(Based on the original registration states; population in 1910, and 
deaths in 1909, 1910 and 1911). 



Age interval. 


Per cent 
(approximate) . 


Age interval. 


Per cent* 
(approximate). 


(1) 


(2) 


(3) 


(4) 


yr. 
0-1 
5-6 
10-11 
15-16 
20-21 
25-26 
30-31 
35-36 
40-41 
45-46 
50-51 


20 
5 

15 
5 

15 
6 
10 
20 
35 
27 
23 


yr. 

55-56 
60-61 
65-66 
70-71 
75-76 • 
80-81 
85-86 
90-91 
95-100 
100-101 


14 

19 

14 

10 

12 

8 

7 

3 

-2 

3 



In infancy the death-rate for males exceeds that for 

females by 20 per cent. Between five and twenty-five years 

of age the differences vary considerably in successive years 

but average about 10 per cent.^ Above age twenty-five 

the male death-rate begins to exceed the female death-rate 

by considerable amounts and this continues to the age of 

forty, when the excess is 35 per cent. After that it steadily 

decreases. In old age the two rates are much alike. It 

must be remembered that these figures are for a certain 

^ The error of population due to concentration on round numbers 
probably accounts for some of these differences. 



EFFECT OF MARITAL CONDITION ON DEATH-RATES 229 



limited area and for a short interval of time and for a par- 
ticular composition of people with respect to nationality, 
birth-rate, and so on. They are to be regarded merely as 
illustrative of the differences between males and females. 
What are the reasons for the differences here shown? 

Effect of marital condition on specific death-rates. — 
Students will find it interesting to compute specific death- 
rates for males and females according to their marital con- 
dition. It will be found that the rates for single men are 
considerably higher than for married men. Between thirty 
and forty years of age they may be nearly twice as high; at 
higher ages the percentage differences become less. The 
death-rates of single females are higher than those of 
married females except that during part of the child-bearing 
period, — say from twenty to forty-five, — the rates are 
higher for married women. 

Professor Walter F. Willcox, of Cornell University, has 
computed the following specific death-rates for New York 
State, the cities of New York and Buffalo excluded, for 
1909-1911, arranged by age-groups and by classes corre- 
sponding to marital condition, as follows: 

TABLE 54 

SPECIFIC DEATH-RATES ACCORDING TO AGE AND 
MARITAL CONDITIONS, NEW YORK, 1909-11 





Males. 


Females. 


Age-group. 


Single. 


Married. 


Widowed or 
divorced. 


Single. 


Married. 


Widowed or 
divorced. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


20-29 
30-39 
40-49 
50-59 
60-69 
70-79 
80- 


6.6 
12.9 
19.5 
28.7 
51.0 
101.4 
204.2 


4.2 

5.9 

9.5 

17.0 

31.9 

72.7 

205.1 


12.0 
14.1 
17.3 
30.5 
48.6 
96.0 
315.7 


4.7 
7.4 
10.0 
19.9 
37.1 
82.2 
279.8 


5.7 

6.3 

8.2 

14.5 

28.1 

61.4 

194.8 


9.4 

9.5 

12.1 

18.8 

38.2 

87.2 

269.8 



230 SPECIFIC DEATH-RATES 

Among the theories suggested in explanation of these 
differences is the effect of leading a better supervised and 
more restrained life among married persons, the better 
economic conditions of the married, the effect of marriage 
selection and the effect of the marriage relation itself. 

Nationality and specific death-rates. — Specific death- 
rates for different ages and sexes are not the same for all 
nationalities. It is very difficult, however, to say how much 
of this is due to racial difference and how much is due to 
environmental conditions; that is, it is hard to separate 
the physiological from the social and economic factors. 
Practically, however, these factors must be considered 
together in discussing nationalities in the United States. 
We see these differences well marked between the negro and 
the white populations of the original registration states. 
The figures in Table 55, taken from Professor Glover's re- 
port, will show this. 

The figures in this table are carried to an unnecessary 
degree of precision so far as this particular point is concerned 
and in the case of the advanced ages for negroes probably 
not even the whole numbers are accurate. The rate for 
male negroes is almost double that for male whites up to 
the age of sixty or thereabouts; above eighty the rate for 
negroes is lower than for whites. Substantially the same 
relations hold for white and colored females. 

It should be noticed that in these various comparisons 
the effect of age is a factor which must never be left out of 
account. 



EFFECT OF AGE COMPOSITION ON DEATH-RATE 231 



TABLE 55 

SPECIFIC DEATH-RATES FOR WHITE AND NEGRO MALES 

United States, Original Registration States, 19 lo 





Rates per 1000. 


Age interval. 






White. 


Negro. 


(1) 


(2) 


(3) 


0-1 


123.26 


219.35 


5-6 


4.71 


8.56 


10-11 


2.38 


5.02 


15-16 


^.83 


7.87 


20-21 


4.89 


11.96 


25-26 


5.54 


12.28 


30-31 


6.60 


14.96 


35-36 


8.52 


17.28 


40-41 


10.22 


21.03 


45-46 


12.64 


23.99 


50-51 


15.53 


31.42 


55-56 


21.50 


39.50 


60-61 


30.75 


50.79 


65-66 


43.79 


64.33 


70-71 


62.14 


83.98 


75-76 


92.53 


112.77 


80-81 


135.75 


131.27 


85-86 


191.11 


179.82 


90-91 


255.17 


201.01 


95-96 


324.86 


227.76 


100-101 


427.46 


336.29 



Effect of the age composition of a population on the 
death-rate. — It is evident also, from our acquired knowl- 
edge of specific death-rates, that the general death-rates of 
two places cannot be reasonably compared unless the age 
composition of the population is substantially the same in 
the two places. The following simple example will make 
this plain: 

Two places, A and B, have the same total population, 
i.e., 50,000; and they have the same specific death-rates at 



232 



SPECIFIC DEATH-RATES 



different ages. 'The ages of the people, however, differ as 
shown in the table. From these figures we may compute 
the general death-rate for each place. 



TABLE 56 

EFFECT OF AGE COMPOSITION OF POPULATION ON 
THE GENERAL DEATH-RATE 



Age. 


Population. 


Specific 

death-rate 

per 1000. 


Computed deaths. 


Computed 

death-rates 

per 1000. 




A 


B 


A 


B 


A ■ 


B 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


0-4 

5-59 

60-79 


10,000 

35,000 

5,000 


20,000 
20,000 
10,000 


25 

10 
60 


250 
350 
300 


500 
200 
600 






Total 


50,000 


50,000 




900 


1300 


18 


26 



In B, a place with a large number of children and old 
people, the rate is 26 per 1000, while in A, a place^'with a 
large middle-aged population, the rate is only 18. This 
is, of course, an exaggerated case, but slight differences in 
age distribution make a greater difference in the general 
death-rate than one would suppose. 

In 1899, according to a report of the U. S. Secretary of 
War, the annual death-rate of soldiers in the Philippines 
was 17.20, while the death-rate of Boston was 20.09, of 
Washington 20.74 and of San Francisco 19.41. The ob-, 
vious inference was that the mortality in the^army com- 
pared favorably with the mortalities of the cities mentioned. 
The facts unstated were that soldiers are picked men in a 
limited age-group while the cities contain a conglomerate 
population. A better comparison would have been one 
between the soldiers and males between 20 and 40 years of 
age in the United States, the usual death-rate for which is 



EFFECT OF AGE COMPOSITION ON DEATH-RATE 233 



less than 10 per 1000. Hence the mortaUty among the 
troops in the Philippines was nearly twice as high as that 
of males of similar age in the United States. 

In 1911 the general death-rate of Chicago was 14.5 and 
that of Cambridge, Mass., was 15.2. Was Chicago the 
healthier city? No, indeed! The following figures show 
that the specific death-rates were lower in Cambridge for 
all ages except the age-intervals of 10-19 years and 65 years 
and over. The reason for Chicago's lower rate was because 
there were relatively more people in Chicago at those 
middle ages where the specific death-rates are naturally 
low. 

TABLE 57 

COMPARISON OF DEATH-RATES IN CAMBRIDGE, MASS., 

AND CHICAGO 



Age in years. 


Per cent of population in 

age-groups. Both sexes. 

1910. 


Specific death-rates per 1000, 
in 1911. 




Cambridge. 


Chicago. 


Cambridge. 


Chicago. 


(1) 


(2) 


(3) 


(i) 


(5) 


Under 5 


10.3 


10.2 


39.1 


39.5 


5-9 


9.1 


8.8 


4.3 


4.7 


10-14 


8.5 


8.6 


3.5 


2.6 


15^19 


8.5 


9.6 


4.6 


3.7 


20-24 


9.9 


11.5 


3.8 


5.3 


25-34 


18.2 


19.7 


5.5 


6.9 


35-44 


15.0 


14.5 


9.0 


11.4 


45-54 


16.0 


9.6 


16.0 


19.3 


55-64 




4.5 


29.4 


35.1 


65-74 


4.5 


2.0 


64.0 


63.6 


75 and over (in- 










cluding unknown) 




1.0 


148.8 


144.2 


Total 


100.0 


100.0 


15.2 


14.5 



Obviously the two general death-rates tell us very little 
that we want to know — that is, not until they have been 
analyzed. 



234 SPECIFIC DEATH-RATES 

Effect of race composition on death-rates. — If differ- 
ent races have different specific death-rates then the 
general death-rates of two places which have different 
percentages of various races cannot be fairly compared. The 
general death-rates of southern cities cannot be fairly com- 
pared with those of northern cities. In 1911 the general 
death-rate in New York City was 15.2; in Washington it 
was 18.7; in New Orleans, 20.4. The death-rate for the 
white population in Washington, however, was only 15.5 
and in New Orleans only 16.6. Even these figures are 
not strictly comparable as they do not take into account 
age distribution. 

Changes in specific death-rates through long periods. — 
We have seen that the general, or gross, death-rates have 
been falling for a long time. Are the same changes occur- 
ring in the specific death-rates at different ages and for dif- 
ferent classes of the population? This is a most important 
question. If we can answer it we shall have come close to 
measuring the effect of our sanitary, hygienic and med- 
ical improvements during recent years. Far too little 
effort has been made to compile statistics of this sort. Let 
us see what we can learn from Massachusetts records. 

In 1830 Lemuel Shattuck computed specific death-rates 
for Boston. It will be interesting to compare these with 
figures for the year 1911, published in the U. S. Mortality 
Statistics by the Bureau of the Census and recast to make 
the age-groups correspond. 



CHANGES IN SPECIFIC DEATH-RATES 



235 



TABLE 58 
SPECIFIC DEATH-RATES, BOTH SEXES, FOR BOSTON 



Age inter- 
val. 


Rate 


per 1000. 


1830. 


1911. 


(1) 


(2) 


(3) 






(approximate) 


0-1 




161 


1-5 




17 


0-5 


59.6 




5-9 


8.1 


4 


10-14 


5.5 


2.4 


15^19 


4.9 


4 


20-29 


10.4 


6 


30-39 


20.1 


10 


40-49 


22.4 


15 


50-59 


29.3 


27 


60-69 


45.8 


52 


70-79 


92.4 


102 


80-89 


162.1 




90- 


321.4 





During the 81 years there has been a marked reduction 
in the specific death-rates at all ages below sixty. In the 
case of children and youths the reduction was as much as one 
half. In 1898 Dr. Samuel W. Abbott, then Secretary of 
the Massachusetts State Board of Health, computed a life 
table for the State ^ for the 3^ears 1893-7 in which the spe- 
cific death-rates were given for certain age-groups. It is 
interesting to compare these with the figures given for 
Massachusetts in the U. S. Life Tables for 1910. 

1 Ann. Rept. 1898, p. 810. 



236 



SPECIFIC DEATH-RATES 



TABLE 59 
SPECIFIC DEATH-RATES FOR MASSACHUSETTS 





Rate per 1000 




Rate per 1000 




1893-7 




1910 


Age-group. 






Age-group. 








Males. 


Females. 


Males. 


Females. 


(1) 


(2) 


(3) 


C4) 


(5) 


(6) 


0-4 


60.12 


52.22 








5-9 


5.69 


5.82 


7-8 


3.37 


3.13 


10-14 


3.11 


3.40 


12-13 


2.27 


2.05 


15-19 


5.29 


5.68 


17-18 


3.43 


3.17 


20-24 


7.48 


7.32 


22-23 


5.16 


4.30 


25-34 


9.33 


8.78 


30-31 


6.60 


5.97 


35-44 


11.19 


10.74 


40-41 


10.00 


8.14 


45-54 


16.67 


14.88 


50-51 


16.05 


12.58 


55^64 


30.42 


26.00 


60-61 


33.15 


27.03 


65-74 


59.67 


51.37 


70-71 


67.91 


56.47 


75-84 


116.20 


99.88 


80-81 


137.43 


123.49 


85-94 


223.50 


184.81 


90-91 


251 .53 


244.90 


95- 


429.20 


367.07 


100-101 


483.90 


392.91 



Here we see the specific death-rates ^till falHng up to 
age sixty. For the later ages there has been a shght tend- 
ency to increase. It should be noticed, however, that the 
age-groups are not quite the same for the two periods. 

In 1830 and also in 1893-7 the specific rates at ages five to 
twenty, or thereabouts, were higher for females than for 
males, but in 1910 the opposite was true. 

If we should make similar comparisons of specific death- 
rates for other places and for different periods we should* 
almost always find that in recent years the rates have been 
falling for all ages below fifty or sixty. 

What have been the reasons for this reduction? Un- 
doubtedly improved sanitary and hygienic conditions, 
advances in medical and surgical science and the arts of 
preventive medicine have tended to reduce the number of 



CHANGES IN SPECIFIC DEATH-RATES 



237 




220 



200 



180 



160 



140 

o 

a 

^120 

-t-> 

cS 

O 
100 



80 







1910 



1870 1880 1890 



1900 



1910 



Specific Death-rates by Age-Groups, Massachusetts, 
1870-1910. 



238 SPECIFIC DEATH-RATES 

cases of sickness and to increase the percentage of recoveries 
of those who are taken sick. This has been especially 
true in the earlier ages. But it must not be forgotten that 
changes in the relative numbers of married and single 
persons in each sex, and of persons of different national- 
ity, have also their influence. A reason for the increase in 
the specific death-rates above fifty or sixty years of age has 
been frequently discussed of late, namely an increase in cer- 
tain degenerative and organic diseases. This is important, 
if true, but it is a difficult thing to prove. 

The fallacy of concealed classification. — Now that we 
have come to appreciate the effect of age, sex, nationality, 
and such factors on death-rates, but especially the factor 
of age, we can better understand what may be called the 
fallacy of concealed classification. If we classify males 
according to occupation we might find that the death- 
rate of bank presidents was higher than that of newsboys; 
but this would not be because of different occupation but 
because of different ages. In classifying by occupation we 
have concealed a grouping by age. If, in classifying the 
employees of the city of Boston or New York by occupation 
we distinguish between policemen and street cleaners, we 
might find that we had concealed a classification by nation- 
ality, the street cleaners being Italians and the policemen 
Irishmen. Similarly in classifying railroad employees into 
conductors and brakemen, we might conceal age differences, 
and under the class of Pullman porters we might conceal a 
nationality difference. When we consider stenographers as 
a separate class we conceal a classification by sex. These 
concealed classifications and groupings are sometimes very 
illusive; they creep into our statistics unawares and upset 
what might otherwise be sound reasoning. Illustrations 
may be found on every hand. Every one who uses statis- 
tics should be continually on the watch for them. 



USE OF SPECIFIC DEATH-RATES 239 

Use of specific death-rates. — It must be evident from 
what has been said that in order to compare the mortahty 
conditions in various places the best way is to compare 
age with age, sex with sex, nationahty with nationahty, or 
in other words to compare the various places, classes and 
groups on the basis of their specific death-rates. To do this 
in great detail involves labor and the use of many figures. 
Hence there has always been a fascination in combining these 
figures so as to obtain a single figure which may be regarded 
as an index of mortality. There are at least two ways of do- 
ing this. If there were such a thing as a standard population 
— and several such standards have been suggested, notably 
the Standard Million (see page 181) — and if we knew the 
specific death-rates by ages and sex for any place, we could 
apply these rates to the standard population and find 
what the general death-rate would have been in the given 
place if the population had been standard. And we might 
do the same for another place and thus obtain figures for 
the death-rates which could be compared with some degree 
of justice. 

When general death-rates are adjusted to a standard 
population in this way the results are called ^' Standardized 
death-rates.' ' Sometimes they have been referred to as 
" corrected " death-rates, but this is a poor use of the word, 
for the process is not one of correcting errors or mistakes and 
the final result is not " correct," for it does not take into 
account all differences in population. Nor is the expression 
" standardized " a good one, because it is not the death- 
rate which is standardized, but only the population. A 
better term is '^ Death-rates adjusted to a Standard Pop- 
ulation." 

In the annual report of the Massachusetts State Board 
of Health for 1902 may be found another method of ^' cor- 
recting " death-rates, used by Dr. Samuel W. Abbott. He 



240 SPECIFIC DEATH-RATES 

took as a standard the specific death-rates of Massachusetts 
by age and sex. He then appUed these to the age and sex 
groups of the cities of the state, to obtain what he called the 
standard death-rate for each place. Then he found the 
ratio between the " standard death-rate " for each place and 
the general death-rate of the state, and called this the " fac- 
tor of correction.'' Finally he multiplied the actual general 
death-rate of each place by this factor to obtain his " cor- 
rected death-rate." The advantage of this method was 
that he did not need to use the age distribution of deaths 
for each place. The method is interesting, but is not one 
for general adoption, because it would be hard to decide on 
a standard of specific death-rates. 

Another way of using specific death-rates is that of con- 
structing what are called life tables. These will be de- 
scribed in Chapter XIV. 

But the best way of using specific death-rates is to use 
them directly. To be sure it means that one must carry 
more figures in one's mind. Instead of having to think of 
one figure for the general death-rate it is necessary to think 
of figures for infant deaths, for the deaths of children, of 
adults and of the aged — • but, after all, are not these the 
really important figures? Statistics are worthless unless 
they can be used. If specific death-rates are more usable 
than general death-rates, we should make the specific rates 
more prominent and educate people to think in terms of 
them. 

Death-rates adjusted to a standard population. — A 
few examples will now be given to show how' general rates 
may be adjusted to a standard population. For the sake 
of simplicity age differences only will be considered. The 
data required are (a) the number of deaths by age-groups 
in the given place; (b) the number of persons living at 
mid-year in the corresponding age-groups; (c) an assumed 



ADJUSTED DEATH-RATES 



241 



standard population for the same age- grouping. First 
of all, therefore, some system of age-grouping must be 
decided upon. Let us take first a simple case, that is, one 
where there are only a few groups. 

On page 226 were given data for New South Wales, from 
which the specific death-rates were computed. Let us 
apply these specific death-rates to the population of Sweden 
in 1890 which we will take as a standard. This is given in 
column (5) of Table 60. For age-group 1-19 years the spe- 
cific rate was 2.78 per 1000; hence, among 398 persons the 
number of deaths would be 0.398 X 2.78 or 1.11 as given 
in column (6). And so for the other age-groups. The 
figures in column (6), therefore, give the number of deaths in 
each group of the standard thousand of population, and 
their sum is the total number of deaths in the standard 
thousand. Hence the death-rate of New South Wales ad- 
justed to the standard population was 13.44. This is 
much higher than the general death-rate, which was only 
9.85. 

TABLE 60 
ADJUSTED DEATH-RATE FOR NEW SOUTH WALES, 1901 



Age-^roup in 

years. 


Population. 


Number of 
deaths in 
one year. 


Specifi c 

death-rate 

per 1000. 


Standard age 

distribution 

per 1000. 


Computed 
deaths per 
1000 of total 
population. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


0-1 

1-19 
20-39 
40-59 
60 and over 


40,500 
704,000 
514,900 
256,600 

89,800 


3,234 
1,960 
2,251 
2,965 
5,400 


79.88 

2.78 

4.37 

11.56 

60.13 


25.5 
398.0 
269.6 
192.3 
114.6 


2.04 
1.11 

1.18 
2.22 
6.89 


Total 


1,605,800 


15,810 


9.85 


1000.0 


13.44 



Why this difference? The answer is found by comparing 
the age distribution of the people of New South Wales with 
the assumed standard population. 



242 



SPECIFIC DEATH-RATES 



TABLE 61 

COMPARISON OF POPULATION DISTRIBUTION OF NEW 
SOUTH WALES WITH THAT OF SWEDEN IN 1890 



Age-group. 


New South Wales. 


Sweden. 




Number. 


Per thousand. 


Per thousand. 


(1) 


(2) 


(3) 


■ (4) 


0-1 
1-19 
30-39 
40-59 
60- 


40,500 
704,000 
514,900 
256,600 

89,800 


24.9 
439.0 
320.0 
160.5 

55.6 


25.5 
398.0 
269.6 
192.3 
114.6 


AU Ages 


1,605,800 


1000.0 


1000.0 



It will be seen that in New South Wales there were fewer 
old persons, for whom the specific death-rates are naturally 
high, but more persons in middle life, for whom the specific 
death-rates are naturally low. This is an extreme case, but 
characteristic of a new population built up by immigration. 
' Let us now take a more complicated situation. 

In 1914 there were 1452 deaths in Cambridge,^ Mass., 
distributed by age as follows: 

TABLE 62 
DISTRIBUTION OF DEATHS: CAMBRIDGE, MASS., 1914 



Age. 


Num- 
ber. 


Age. 


Num- 
ber. 


Age. 


Num- 
ber. 


Age. 


Num- 
ber. . 


(1) 


(2) 


(1) 


(2) 


(1) 


(2) 


a) 


(2) 


[0-1] 

0-5 

5-9 

10-14 

15-19 


[243] 

340 

20 

26 

33 


20-24 
25-29 
30-34 
35-39 
40-44 


43 
49 
62 

58 
56 


45-49 
50-54 
55-59 
60-64 
65-69 


90 

83 

73 

107 

109 


70-74 
75-79 
80-84 
85-89 
90-94 
95-99 


110 
72 
66 
33 
18 
4 



U. S. Mortality Statistics, 1914, p. 264. 



ADJUSTED DEATH-RATES 



243 



The Standard Million^ will be taken as the standard of 
population. It is necessary to take an age-grouping which 
will correspond to this, and find the number of persons in 
Cambridge in 1914 in each of these groups. There was no 
census in Cambridge in 1914, but in 1910 the population 
was 104,839, in 1900 it was 91,886. The estimated popu- 
lation July 1, 1914, was 110,357. In 1910 the age distri- 
bution of the people of Cambridge was given by the census. 
It was as follows (columns 1, 2 and 3) : 



TABLE 63 
PERSONS LESS THAN STATED AGE: CAMBRIDGE, MASS. 



Age. 


Actual number of 
persons in 1910 


Per cent. 


Computed number of 
persons in 1914. 


(1) 


(2) 


(3) 


(4) 


1 

5 
10 
15 
20 
25 
35 
45 
65 
100 
Unknown 


2,323 
10,802 
20,273 ' 
29,165 
37,095 
47,503 
66,678 
82,404 
99,136 
104,778 
61 


2.3 
10.4 
19.4 
27.9 
36.4 
46.4 
64.6 
79.6 
95.6 
99.4 

0.6 


2,430 

11,500 

21,400 

30,800 

40,200 

51,200 

70,500 

88,000 

105,700 

110,280 

77 


Total 


104,839 


100.0 


110,357 



It may be fairly assumed that the percentages of column 
3 for 1910 apply also with no great change to 1914. By 
multiplying 110,357, therefore, by these percentages we 
get the following numbers of persons in each group for 
1914 (column 4). 

The figures in column (4) may be redistributed in any 

1 See p. 181. 



244 



SPECIFIC DEATH-RATES 



desired age-grouping as described on p. 172. In this way 
the figures in column (2) of the following table were ob- 
tained : 

TABLE 64 

ADJUSTED DEATH-RATES FOR CAMBRIDGE, MASS. 



Age-jroup. 


Estimated 
population in 

1914 
(approximate). 


Number of 

deaths in 

1914. 


Specific 

death-rate 

per 1000. 


Standard 

age distribution 

per 1000. 


Computed 
deaths, j 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


0-4 
5-9 
10-14 
15-19 
20-24 
25-34 
35-44 
45-54 
55-64 
65-74 
75- 


11,500 

9,900 

9,400 

9,400 

11,000 

19,200 

17,400 

11,600 

5,800 

3,100 

2,100 


340 

20 

26 

33 

43 

111 

114 

173 

180 

219 

193 


29.5 
2.02 
2.76 
3.51 
3.91 
5.78 
6.53 
14.9 
31.1 
70.6 
91.8 


114.262 

107.209 

102.735 

99.796 

95.946 

161.579 

122.849 

89.222 

59.741 

33.080 

13.581 


0.380 
0.217 
0.284 
0.350 
0.374 
0.935 
0.803 
1.330 
1.856 
2.330 
1.246 


Total 


110,400 


1452 


13.15 


1000.000 


13 . 105 



From columns (2) and (3) the specific death-rates are 
obtained (column 4), and these appHed to the standard 
age distribution (column 5) give the number of computed 
deaths in each age-group (column 6). Their sum gives 
13.1, which is the death-rate adjusted to the standard 
age distribution. We have done all this work to get a 
result which differs but fractionally from the general, or 
crude death-rate, i.e., 13.15. Not worth while? Yes, it 
is if we are to use a death-rate at all. It was only because 
the age distribution of the Cambridge population happened 
to be so near that of the standard milhon that the two 
death-rates came so close together. In another case the 
result might be very different. 



ADJUSTED DEATH-RATES 



245 



A fair criticism of this last computation would be that 
the age-groupings below age five and above middle age are 
too wide, for it is in these groups where the specific death- 
rates are highest. Dr. Wm. L. Holt, C.P.H. (School of 
Public Health, Harvard University and Mass. Inst, of 
Tech.), investigated this subject of grouping and concluded 
that seven properly selected groups would give results 
which compared well with those obtained by using the 
eleven groups of the Standard Million. The author be- 
lieves that even five well-chosen groups would suffice, but 
the matter is one which needs free discussion. Certainly 
something more convenient than the Standard Million is 
possible. 

TABLE 65 

COMPUTED DEATH-RATES IN BOSTON AND CAM- 
BRIDGE, 1905 

(Computations by Dr. Wm. L. Holt) 



Boston. 











Adjusted rates 


per 1000. 


Age- 


Popula- 
tion. 


Deatha. 


Specific 
death-rate. 








group. 


Eleven 


Nine 


Seven 


Six 










groups. 


groups. 


groups. 


groups. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


0-4 


52,152 


3128 


60.1 


6.850 


6.850 


6.850 


6.850 


5-9 


54,091 


253 


4.68 


0.501 


0.501 1 






10-14 
15-19 


48,694 
47,608 


157 

218 


3.22 

4.58 


0.331 / 
0.457 j 


0.785 [ 


1.963 


1.963 


20-24 


57,421 


380 


6.61 


0.634 


0.634 J 






25-34 


119,632 


1070 


8.95 


1.441 


1.441 1 


2.840 


2.840 


35-44 


95,946 


1081 


11.28 


1.388 


1.388^ 


45-54 


58,810 


1255 


21.4 


1.910 


1.910 


1.9101 


4.135 


55-64 


33,602 


1308 


38.9 


2.325 


2.325 


2.325i 


65-74 


16,711 


1213 


72.6 


2.403 I 
1.980 J 
20.220 


4.802 


2.403 


2.403 


75- 


6,413 


937 


146.0 


1.980 


1.980 


Total 


20.636 


20.271 


20.171 



(Continued on next page.) 



246 



SPECIFIC DEATH-RATES 



• 




Cambridge. 






Age- 


Popula- 


Deaths. 


Specific 


Adjusted rates per 1000. 


group. 


tion. 




death-rate. 












Eleven groups. 


Seven groups. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


0-4 


9,088 


412 


45.3 


5.176 


5.176 


5-9 


9,096 


27 


2.96 


0.317-1 




10-14 


8,078 


20 


2.48 


0.255 


1.468 


15-19 


8,512 


34 


4.00 


0.399 


20-24 


10,789 


51 


4.72 


0.452 J 




25-34 


18,671 


130 


6.97 


1.125 ( 
1 . 127 1 


2 2^3 


35-44 


14,148 


130 


9.19 




45-54 


9,267 


133 


14.35 


1.280 


1.280 


55-64 


5,628 


165 


29.4 


1.755 


1.755 


6.5-74 


2,864 


155 


54.1 


1.790 


1.790 


75- 


1,251 


179 


143.2 


1.950 


1.950 


Total 


15.626 


15.672 



Examples of death-rates adjusted to a standard popu- 
lation. — The U. S. Mortality Statistics give numerous 
examples of death-rates adjusted to the Standard Million. 

Let us first of all compare Cambridge, Mass., and Chicago, 

111. 

TABLE 66 



City. 


Death-rate, 1911. 


Gross. 


Adjusted. 


(1) 


(2) 


(3) 


Cambridge, Mass. 
Chicago, 111. 


15.2 
14.5 


15.4 
16.4 



Here again we see that adjustment of the Cambridge rate 
changes it but little,^ while that of Chicago was increased 
by 1.9, making the adjusted rate higher than that of 
Cambridge. Why? 

1 In this computation sex as well as age was considered. 



EXAMPLES OF ADJUSTED DEATH-RATES 



247 



In every instance in the following table the adjusted 
death-rate exceeded the gross death-rate, the excesses 
ranging from 1 to 18 per cent and averaging 8.4 per cent. 
As would naturally be expected the differences were less 
in the older cities of the East than in the newer cities 
of the West, but New York, Pittsburgh and a few others 
with large numbers of recent immigrants were exceptions 
to this rule. The following figures illustrate this: 

TABLE 67 

COMPARISON OF GROSS AND ADJUSTED DEATH-RATES 
FOR CERTAIN CITIES 







Death-rates per 1000. 


City. 
















Gross. 


Adjusted. 


Difference. 


(1) 


(2) 


(3) 


(4) 


New Haven, Conn. 


16.7 


17.7 


1.0 


Boston, Mass. 


17.1 


17.9 


0.8 


New York, N. Y. 


15.2 


17.2 


2.0 


Pittsburgh, Pa. 


14.9 


16.9 


2.0 


Cleveland, Ohio 


13.8 


15.3 


1.5 


Chicago, 111. 


14.5 


16.4 


1.9 


Spokane, Wash. 


11.6 


13.7 


2.1 


Seattle, Wash. 


8.8 


10.4 


1.6 



Adjustment to a standard population tends to equalize 
the death-rates in different places. The rural districts of 
New England contain a large percentage of persons of ad- 
vanced age. This tends to cause the adjusted rate to be 
lower than the gross rate. Taking figures for entire states 
we find this to be true, as the following figures show. In 
the western 'states this difference is not as marked, as they 
have not suffered by emigration as have the New England 
States. 



248 



SPECIFIC DEATH-RATES 



TABLE 68 

COMPARISON OF GROSS AND ADJUSTED DEATH-RATES 
FOR CERTAIN STATES 







Death-rates per 1000. 


state. 








Gross. 


Adjusted. 


Difference. 


(1) 


(2) 


(3) 


(4) 


Massachusetts 


15.3 


15.0 


-0.3 


New Hampshire 


17.1 


14.2 


-2.9 


Maine 


16.1 


13.0 


-3.1 


Connecticut 


15.4 


14.8 


-0.6 


Indiana 


12.9 


12.3 


-0.6 


Kentucky- 


13.2 


13.4 


0.2 


Michigan 


13.2 


12.4 


-0.8 


Minnesota 


10.5 


10.8 


0.3 


Missouri 


13.1 


13.1 


0.0 


Montana 


10.2 


11.6 


1.4 



The following figures show the relation between the 
crude and adjusted death-rates for various countries: 



ADJUSTMENT FOR RACIAL DIFFERENCES 249 



TABLE 69 

COMPARISON OF GROSS AND ADJUSTED DEATH-RATES 
FOR CERTAIN COUNTRIES 













Ratio of 






Death-rates per 1000. 


adjusted 


Country. 


Year. 








rate 
to that of 


. 








England 






Gross. 


Adjusted. 


Difference. 


and Wales. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


Russia 


1896-1898 


32.80 


28.61 


-4.19 


166.7 


Spain 


1900-1902 


27.63 


26.53 


-1.10 


154.6 


Austria 


189&-1901 


24.83 


23.12 


-1.71 


134.7 


Italy 


1900-1902 


22.72 


20.23 


-2.49 


117.9 


Germany 


1901 


20.84 


19.52 


-1.32 


113.8 


U. S. (Registra- 


1900 


17.55 


18.05 


0.50 


105.2 


tion area) 












Scotland 


1900-1902 


17.91 


17.61 


-0.30 


102.6 


France 


1900-1902 


20.80 


17.50. 


-3.30 


102.0 


England & Wales 


1900-1902 


17.16 


17.16 


0.00 


100.0 


Switzerland 


1899-1901 


18.22 


16.86 


-1.36 


98.3 


Belgium 


1899-1901 


18.53 


16.78 


-1.75 


97.8 


Ireland 


1900-1902 


18.27 


16.59 


-1.68 


96.7 


Netherlands 


1898-1900 


17.32 


15.40 


-1.92 


89.7 


Sweden 


1899-1901 


16.78 


13.88 


-2.90 


80.9 


New South Wales 


1900-1902 


11.72 


13.10 


1.38 


76.3 


Victoria 


1900-1902 


13.12 


13.08 


-0.04 


76.2 


South Australia 


1900-1902 


11.02 


11.73 


0.71 


68.4 



Adjustment for racial differences. — In certain parts 
of the United States, especially in the South, the crude 
death-rates are absolutely useless for purposes of com- 
parison unless allowance is made for the number of colored 
persons at different ages. The specific death-rates for col- 
ored persons are higher at all ages than for white persons, 
as the following figures for the U. S. registration states in 
1900 show: 



250 



SPECIFIC DEATH-RATES 



TABLE 70 

COMPARISON OF SPECIFIC DEATH-RATES FOR WHITE 
AND COLORED PERSONS 





Death-rates per 1000 (exclusive 






of still-births). 


Ratio of colored 


Age-group (both sexes). 




to white death- 








rate. 




Native white. 


Colored. 




(1) 


(2) 


(3) 


(4) 


0-4 


49.1 


106.4 


2.17 


5-9 


4.5 


8.9 


1.98 


10-14 


2.9 


9.0 


3.10 


15-19 


4.7 


11.4 


2.43 


20-24 


6.8 


11.6 


1.71 


25-34 


8.2 


12.2 


1.49 


35-44 


9.6 


15.0 


1.56 


45-54 


12.7 


24.5 


1.93 


55-64 


22.6 


42.5 


1.88 


65-74 


50.4 


69.5 


1.38 


75 


138.5 . 


143.3 


1.03 


Crude death-rate 


16.5 


25.0 


1.52 



The following figures for the cities of Washington, Balti- 
more and New Orleans show the necessity of taking into ac- 
count these striking differences between the white and colored , 
people : 



DEATH-RATES FOR PARTICULAR DISEASES 251 



TABLE 71 

ADJUSTED DEATH-RATES FOR CITIES HAVING LARGE 
COLORED POPULATIONS 





Death-rates per 1000 (both sexes), 1911. 




Gross. 


Adjusted. 


Difference. 


(1) 


(2) 


(3) 


(4) 


Washington, D. C. 
White 
Colored 
Total 

Baltimore, Md. 
White 
Colored 
Total 

New Orleans, La. 
White 
Colored 
Total 


15.5 
26.6 
18.7 

16.2 
30.9 
18.4 

16.6 
31.2 
20.4 


14.6 
30.5 
18.9 

16.7 
35.4 
19.4 

17.5 
34.0 
21.8 


-0.9 
3.9 
0.2 

0.5 
4.5 
1.0 

0.9 

2.8 
1.4 



Death-rates for particular diseases. — Death-rates for 
particular diseases are computed in the same way as other 
specific death-rates. The numerator of the ratio is limited 
to the disease in question. The denominator may be the 
entire population, or it may be confined to some specific 
part of it. In order to avoid the use of .too many decimals 
it is well to express the death-rates for particular diseases as 
so many per 100,000 instead of so many per 1000. This 
practice is becoming universal. The use of 10,000 as a 
base should be avoided. 

If all of the deaths from typhoid fever be compared with 
the total mid-year population, we have the general typhoid 
fever death-rate of the place. General rates for particular 
diseases are much used and have practical value. Specific 



252 SPECIFIC DEATH-RATES 

rates in whichMeaths from typhoid fever in a given age- 
group are compared with the population in the same age- 
group are sometimes computed, but are useful only when 
the numbers involved are large. 

Special death-rates. — In epidemiological studies it is 
necessary to compute death-rates in all sorts of ways, to 
separate the people into classes according to where and how 
they live, according to their occupation or their exposure 
to certain risks. This causes us to deal with many special 
rates. 

In studying birth statistics we may find the general 
birth-rate, by taking the ratio between the number of 
births and the total population. But we may also desire 
to find the ratio between births and women of child- 
bearing age, or between births and married women of 
child-bearing age. 

In interpreting all of these many sorts of rates and ratios 
the principles already outlined hold good. We must see 
that the data compared are logically comparable, that there 
are no concealed classifications and that the rules of pre- 
cision are not violated. 



EXERCISES AND QUESTIONS 

1. Are the changes in age-composition from decade to decade in 
Massachusetts sufficient to explain a considerable part of the falling 
general death-rate of the state, assuming the specific death-rates by 
ages to remain constant? 

2. Compute the specific death-rates by sex and age-groups for three 
Massachusetts cities for 1910, obtaining data from the census and 
registration reports. 

3. Compare the specific death-rates by age-groups for white and 
colored persons in some southern city for some selected year. 

4. Adjust the death-rate of some western city in 1910 to the Swedish 
standard of population. 



EXERCISES AND QUESTIONS 253 

5. Repeat this computation using the standard miUion as a basis of 
adjustment. 

6. Select from the MortaUty Reports examples of the need of adjust- 
ment of death-rates of cities for purposes of comparison. 

7. Adjust the death-rates of some selected city to the basis of the 
Standard Million for 1915, 1910, 1905, 1900 and as far back as record 
can be obtained. 



CHAPTER VIII 
CAUSES OF DEATH 

Nosography. — The description and systematic classifi- 
cation of disease is called nosography. The word is derived 
from the Greek word nosos, which means sickness, or disease. 
(The word is pronounced noss'ography, not noze-ography.) 

Nosology. — The science of classifying disease is similarly 
called nosology. 

The purpose of nosology. — At one time it was thought 
that a knowledge of nosology was necessary for the practical 
treatment of disease. Many systems were proposed and 
abandoned. Today the idea has few, if any, supporters. 

Nosology is of great importance as one of the foundation 
stones of our modern structure of vital statistics. Without 
uniform definitions of disease which furnish us with adequate 
statistical units our statistics would be worthless. It is because 
of changes in our definitions of disease that we fall into so 
many errors in comparing past conditions with those of the 
present day. Such changes are inevitable as medical science 
advances, but they ought to be universally recognized when 
they are made. 

Dr. William Farr was one of the first to recognize the 
importance of '^ statistical nosology." 

History of nosography. — Nosography emerged from its 
former chaotic condition in 1893 when the use of the Inter- 
national Classification of Diseases and Causes of Death was 
begun. .This was due chiefly to the labors of Dr. Jacques 
Bertillon of France. 

254 



INTERNATIONAL LIST OF THE CAUSES OF DEATH 255 

In 1853 Dr. William Farr and Dr. Marc d'Espine, of 
Geneva, had been selected by the First Statistical Congress, 
which met at Brussels, to present a report on the subject. 
The list of diseases reported by them was adopted in Paris in 
1855, in Vienna in 1857, and was translated into six languages. 
It was revised several times between 1864 and 1886. In 1893 
the International Statistical Institute, the successor of the 
Statistical Congress, met in Chicago and adopted this list 
with some changes. Provision was made for decennial 
revisions by an International Commission, and such revisions 
were made in Paris in 1900 and again in 1909, the latter a 
year earlier in order that the new list might be used in the 
censuses of 1910. The present list is intended to stand un- 
changed until 1919. In 1898 the International List was 
endorsed by the American Public Health Association. Eng- 
land adopted the list in 1911. It is used by all English and 
Spanish speaking countries, but it is not yet universal. A 
few of our own states do not follow it exactly, namely: 
Alabama, New Hampshire, New Mexico, Rhode Island and 
West Virginia. 

International list of the causes of death. — In 1911 the 
U . S. Bureau of the Census published a Manual of 297 pages, 
being a revision of a former manual published in 1902. This 
list is the present standard for the United States and has 
come to be almost universally used. This manual is very 
complete. It gives the standard list of the causes of death, 
with synonyms, and is indexed alphabetically as well as 
according to the chosen classification. 

The Bureau of the Census also publishes a Physician's 
Pocket Reference to the International List of the Causes of 
Death, which can be obtained without charge by anyone who 
makes request of the Director of the Census, Washington, 
D. C. This is a small pamphlet of 28 pages, vest pocket 
size. 



256 



CAUSES OF DEATH 



Classification of diseases in 1850. — Dr. Farf classified 

diseases as follows: 

Class I. Epidemic, Endemic and Contagious diseases (Zymotici). 
Order 1 . Miasmatic diseases, — small-pox, ague, etc. 
Order 2. Enthenic diseases, — syphilis, glanders. 
Order 3. Dietetic diseases, — scurvy, ergotism. 
Order 4. Parasitic diseases. 
Class II. Constitutional Diseases (Cachectici) . 

Order 1. Diathetic diseases, — gout, dropsy, cancer, etc. 
Order 2. Tubercular diseases, — scrofula, consumption. 

Class III. Local Diseases (Monorganici). 

Order 1. Diseases of the brain. 

Order 2. Diseases of the circulation. 

Order 3. Diseases of respiration. 

Order 4. Diseases of digestion. 

Order 5. Diseases of the urinary system. 

Order 6. Diseases of reproduction. 

Order 7. Diseases of locomo: ive system. 

Order 8. Diseases of integumentary system. 

Class IV. Developmental Diseases (Metamorphici). 

Class V. Violent Deaths, or Diseases (TMnaiia). 

It is extremely interesting to study this list in detail as 
given in the 16th Annual Report of the Registrar General 
of England, Appendix, pp. 71-79. 

Present classification. — The list recognizes 189 causes 
of death, which are divided into fourteen classes. It is not 
claimed that these are all of the possible causes. For con- 
venience of reference and tabulation each of these diseases 
is given a number. The following is the list as given in the * 
Physician's Pocket Reference. It is recommended that only 
the names printed in heavy type be used. The terms in 
italics are indefinite or otherwise undesirable. An abridged 
list of causes of death useful for annual reports of health 
departments may be found on page 



PRESENT CLASSIFICATION 257 

INTERNATIONAL LIST OF CAUSES OF DEATH 

(I. — General Diseases) 

1. Typhoid fever. 

2. Typhus fever. 

3. Relapsing fever. [Insert "(spirillum)."] 

4. Malaria. 

5. Smallpox. 

6. Measles. 

7. Scarlet fever. 

8. Whooping cough. 

9. Diphtheria and croup. 

10. Influenza. 

11. Miliary fever. [True Febris miliaris only.] 

12. Asiatic cholera. 

13. Cholera nostras. 

14. Dysentery. [Amebic? Bacillary? Do not report ordinary 

diarrhea and enteritis (104, 105) as dysentery.] 

15. Plague. 

16. Yellow fever. • 

17. Leprosy. 

18. Erysipelas. [State also cause; see Class XIII.] 

19. Other epidemic diseases: 

Miunps, 

German measles, 

Chicken-pox, 

Rocky Mountain spotted (tick) fever, 

Glandular fever, etc. 

20. Purulent infection and septicemia. [State also cause; see Classes 

VII and XIII especially.] 

21. Glanders. 

22. Anthrax. 

23. Rabies. 

24. Tetanus. [State also cause; see Class XIII.] 

25. Mycoses. [Specify, as Actinomycosis of lung, etc.] 

26. Pellagra. 

27. Beriberi. 

28. Tuberculosis of the lungs. 

29. Acute miliary tuberculosis. 

30. Tuberculous meningitis. 



258 CAUSES OF DEATH 

31. Abdominal tuberculosis. 

32. Pott's disease. [Preferably Tuberculosis of spine.] 

33. White swellings. [Preferably Tuberculosis of joint.] 

34. Tuberculosis of other organs. [Specify organ.] 

35. Disseminated tuberculosis. [Specify organs affected.] 

36. Rickets. 

37. Syphilis. 

38. Gonococcus infection. 

39. Cancer ^ of the buccal cavity. [State part.] 

40. Cancer ^ of the stomach, liver. 

41. Cancer ^ of the peritoneum, intestines, rectum. 

42. Cancer^ of the female genital organs. [State organ.] 

43. Cancer ^ of the breast. 

• 44. Cancer ^ of the skin. [State part.] 

45. Cancer ^ of other or unspecified organs. [State organ.] 

46. Other tumors (tumors of the female genital organs excepted.) 

[Name kind of tumor and organ affected. Malignant?] 

47. Acute articular rheumatism. [Always state " rheumatism " as 

acute or chronic] 

48. Chronic rheumatism [preferably Arthritis deformans] and gout. 

49. Scurvy. 

50. Diabetes. ' [Diabetes mellitus.] 

51. Exophthalmic goiter. 

52. Addison's disease. 

53. Leukemia. 

54. Anemia, chlorosis. [State form or cause. Pernicious?] 

55. Other general diseases: 

Diabetes insipidus, 
Purpura haemorrhagica, etc. 

56. Alcoholism (acute or chronic). 

57. Chronic lead poisoning. [State cause. Occupational?] 

58. Other chronic occupational poisonings. [State exact name of 

poison, whether the poisoning was chronic and due to oc- 
cupation, and also please be particularly careful to see that 
the Special Occupation and Industry are fully stated. If 

^ '' Cancer and other malignant tumors." Preferably reported as 

Carcinoma of , Sarcoma of , Epithelioma of , etc., stating 

the exact nature of the neoplasm and the organ or part of the body first 
affected. 



PRESENT CLASSIFICATION 



259 



the occupation stated on the certificate is not that in which 
the poisoning occurred, add the latter in connection with the 
statement ;of cause of death, e.g., *' Chronic occupational 
phosphorus necrosis (dipper, match factory, white phos- 
phorus)." Give full details, including pathologic conditions 
contributory to death. Following is a List of Industrial 
Poisons {Bull. Bureau of Labor, May, 1912) to which the 
attention of physicians practicing in industrial communities 
should be especially directed: 



Acetaldehyde, 

Acridine, 

Acrolein, 

Ammonia, 

Amyl acetate, 

Amyl alcohol, 

Aniline, 

Aniline dyestuffs [name]. 

Antimony compounds [name] 

Arsenic compounds [name], 

Arseniureted hydrogen. 

Benzine, 

Benzol, 

Carbon dioxide. 



Hydrochloric acid, 
Hydrofluoric acid, 
Lead (57), 
Manganese dioxide, 
Mercury, 
Methyl alcohol. 
Methyl bromide, 
Nitraniline, 
Nitrobenzol, 
Nitroglycerin, 
Nitronaphthalene, 
Nitrous gases. 
Oxalic acid, 
Petroletun, 
Phenol, 



Carbon disulphide. 
Carbon monoxide (coal vapor, il- Phenylhydrazine, 
luminating water gas, producer Phosgene, 



gas). 
Chloride of lime. 
Chlorine, 

Chlorodinitrobenzol, 
Chloronitrobenzol, 
Chromium compounds [name] 
Cyanogen compounds [name], 
Diazomethane, 
Dimethyl sulphate, 
Dinitrobenzol, 
Formaldehyde, 



Phosphorus (yellow or white), 

Phosphorus sesquisulphide, 

Phosphureted hydrogen. 

Picric acid. 

Pyridine, 

Sulphur chloride. 

Sulphur dioxide, 

Sulphureted hydrogen. 

Sulphuric acid. 

Tar, 

Turpentine oil. 



Not all substances in the preceding list are likely to be reported 
as causes of death, but the physician should be familiar with it in 
order to recognize, and to report, if required, cases of iUness, and 



260 CAUSES OF DEATH 

should also be on the alert to discover new forms of industrial poi- 
soning not heretofore recognized. In the Bulletin cited full details 
may be found as to the branches of industry in which the poisoning 
occurs, mode of entrance into the body, and the symptoms of poi- 
soning. Attention should also be called to industrial infection, e.g., 
Anthrax (22), and the influence of gases and vapors, dust, or unhygienic 
industrial environment. 

59. Other, chronic poisonings: 

Chronic morphinism, 
^ Chronic cocainism, etc. 

(II. — Diseases of the Nervous System and of the Organs of 

Special Sense) 

60. Encephalitis. 

61. Meningitis: 

Cerebrospinal fever or Epidemic cerebrospinal meningitis, 
Simple meningitis. [State cause.] 

62. Locomotor ataxia. 

63. Other diseases of the spinal cord: 

Acute anterior poliomyelitis. 
Paralysis agitans, 
Chronic spinal muscular atrophy. 
Primary lateral sclerosis of spinal cord. 
Syringomyelia, etc. 

64. Cerebral hemorrhage, apoplexy. 

65. Softening of the brain. [State cause.] 

66. Paralysis without specified cause. [State form or cause.] 

67. General paralysis of the insane. 

68. Other forms of mental alienation. [Name disease causing death. 

Form of insanity should be named as contributory cause 
only, unless it is actually the disease causing death.] 

69. Epilepsy. 

70. Convulsions (nonpuerperal). [State cause.] 

71. Convulsions of infants. [State cause.] 

72. Chorea. 

73. Neuralgia and neuritis. [State cause.] 

74. Other diseases of the nervous system. [Name the disease.] 

75. Diseases of the eyes and their annexa. [Name the disease.] 

76. Diseases of the ears. [Name the disease.] 



PRESENT CLASSIFICATION 261 

(III. — Diseases of the Circulatory System) 

77. Pericarditis. [Acute or chronic; rheumatic (47), etc.] 

78. Acute endocarditis. [Cause? Always report " endocarditis " or 

" myocarditis " as acute or chronic. Do not report when 
mere terminal condition.] 
Acute myocarditis. 

79. Organic diseases of the heart: [Name the disease.] 

Chronic valvular disease, [Name the disease.] 
Aortic insufficiency, 

Chronic endocarditis, [See note on (78).] 
Chronic myocarditis, [See note on (78).] 
Fatty degeneration of heart, etc. 

80. Angina pectoris. 

81. Diseases of the arteries, atheroma, aneurism, etc. 

82. EmboUsm and thrombosis. [State organ. Puerperal (139)?] 

83. Diseases of the veins (varices, hemorrhoids, phlebitis, etc.). 

84. Diseases of the lymphatic system (lymphangitis, etc.). [Cause? 

Puerperal?] 

85. Hemorrhage; other diseases of the circulatory system. [Cause? 
Pulmonary hemorrhage from Tuberculosis of lungs (28)? Puer- 
peral?] 

(IV. — Diseases of the Respiratory System) 

86. Diseases of the nasal fossae. [Name disease.] 

87. Diseases of the larynx. [Name disease. Diphtheritic?] 

88. Diseases of the thyroid body. [Name disease.] 

89. Acute bronchitis. ] [Always state as acute or chronic. Was it 

90. Chronic bronchitis. J tuberculous?] 

91. Bronchopneumonia. [If secondary, give primary cause.] 

92. Pneumonia. [If lobar, report as Lobar pneiunonia.] 

93. Pleurisy. [Cause? If tuberculous, so report (28).] 

94. Pulmonary congestion, pulmonary apoplexy. [Cause?] 

95. Gangrene of the lung. 

96. Asthma. [Tuberculosis?] 

97. Pulmonary emphysema. 

98. Other diseases of the respiratory system (tuberculosis excepted). 

[Such indefinite returns as " Lung trouble," " Pulmonary hem- 
orrhage," etc., compiled here, vitiate statistics. Tuberculosis 
of lungs (28)? Name the disease.] 



262 CAUSES OF DEATH 

"' (V. — Diseases of the Digestive System) 

99. Diseases of the mouth and annexa, [Name disease.] 

100. Diseases of the pharynx. [Name disease. Diphtheritic?] 

Streptococcus sore throat. 

101. Diseases of the esophagus. [Name disease.] 

102. Ulcer of the stomach. 

103. Other diseases of the stomach (cancer excepted). [Name 

disease. 'Avoid such indefinite terms as " Stomach trouble," 
" Dyspepsia," " Indigestion," " Gastritis," etc., when used 
vaguely.] 

104. Diarrhea and enteritis (under 2 years). 

105. Diarrhea and enteritis (2 years and over) . 

106. Ankylostomiasis. [Better, for the United States, Hookworm 

disease or Uncinariasis.] 

107. Intestinal parasites. [Name species.] 

108. Appendicitis and typhlitis. 

109. Hernia, intestinal obstruction. [State form and whether stran- 

gulated.] 

Strangulated inguinal hernia (operation), 

Intussusception, 

Volvulus, etc. 

110. Other diseases of the intestines. [Name disease.] 

111. Acute yellow atrophy of the liver. 

112. Hydatid tumor of the liver. 

113. Cirrhosis of the liver. 

114. Biliary calculi. 

115. Other diseases of the liver. [" Ldver complaint " is not a satis- 

factory return.] 

116. Diseases of the spleen. [Name disease.] 

117. Simple peritonitis (nonpuerperal). [Give cause] 

118. Other diseases of the digestive system (cancer and tuberculosis 

excepted). [Name disease.] 

(VI. NONVENEREAL DISEASES OF THE GeNITO-UrINARY SySTEM 

AND Annexa) 

119. Acute nephritis. [State primary cause, especially Scarlet fever, 

etc. Always state " nephritis " as acute or chronic] 

120. Bright's disease. [Better, Chronic interstitial nephritis. Chronic 

parenchymatous nephritis, etc. Never report mere names of 
symptoms, as " Uremia" " Uremic coma," etc. See also 
note on (119).] 



PRESENT CLASSIFICATION 263 

121. Chyluria. 

122. Other diseases of the kidneys and annexa. [Name disease.] 

123. Calculi of the urinary passages. [Name bladder, kidney.] 

124. Diseases of the bladder. [Name disease.] 

Cystitis. [Cause?] 

125. Diseases of the urethra, urinary abscess, etc. [Name disease. 

Gonorrheal (38)?] 

126. Diseases of the prostate. [Name disease.] 

127. Nonvenereal diseases of the male genital organs. [Name disease.] 

128. Uterine hemorrhage (nonpuerperal). [Cause?] 

129. Uterine tumor (noncancerous). [State kind.] 

130. Other diseases of the uterus. [Name disease.] 

Endometritis. [Cause? Puerperal (137)?] 

131. Cysts and other tumors of the ovary. [State kind.] 

132. Salpingitis and other diseases of the female genital organs. 

[Name disease. Gonorrheal (38)? Puerperal (137)?] 

133. Nonpuerperal diseases of the breast (cancer excepted) . [Name 

disease. ] 

(VII. — The Puerperal State) 

Note. — The term puerperal is intended to include pregnancy, 
parturition, and lactation. Whenever parturition or miscarriage has 
occurred within one month before the death of the patient, the fact 
should be certified, even though childbirth may not have contributed 
to the fatal issue. Whenever a woman of childbearing age, especially 
if married, is reported to have died from a disease which might have been 
puerperal, the local registrar should require an explicit statement from the 
reporting physician as to whether the disease was or was not puerperal 
in character. The following diseases and symptoms are of this class: 

Abscess of the breast, Metroperitonitis, 

Albuminuria, Metrorrhagia, 

Cellulitis, Nephritis, 

Coma, _ Pelviperitonitis, 

■ Convulsions, Peritonitis, 

Eclampsia, Phlegmasia alba dolens, 

Embolism, Phlebitis, 

Endometritis, Pyemia, 

Gastritis, Septicemia, 

Hemmorrhage {uterine or Sudden deaths 

unqualified), Tetanus, 

Lifmphangitis, Thrombosis, 

Metritis, Uremia. 



264 CAUSES OF DEATH 

Physicians are requested always to write Puerperal before the above 
terms and others that might be puerperal in character, or to add in 
parentheses (Not puerperal), so that there may be no possibility of error 
in the compilation of the mortality statistics; also to respond to the 
requests of the local registrars for additional information when, inad- 
vertently, the desired data are omitted. The value of such statistics 
can be greatly improved by cordial cooperation between the medical 
profession Tand the registration officials. If a physician will not write 
the true statement of puerperal character on the certificate, he may 
privately communicate that fact to the local or state registrar, or write 
the number of the International List under which the death should be 
compiled, e.g., " Peritonitis (137)." 

134. Accidents ^ of pregnancy: [Name the condition.] 

Abortion, [Term not used in invidious sense; Criminal abor- 
tion should be so specified (184).] 
Miscarriage. 
Ectopic gestation. 
Tubal pregnancy, etc. 

135. Puerperal hemorrhage. 

136. Other accidents ^ of labor: [Name the condition.] 

Caesarean section. 

Forceps application, 

Breech presentation, 

Symphyseotomy, 

Difficult labor, 

Rupture of uterus in labor, etc. 

137. Puerperal septicemia. 

138. Puerperal albuminuria and convulsions. 

139. Puerperal phlegmasia alba dolens, embolus, sudden death. 

140. Following childbirth {not otherwise defined). [Define.] 

141. Puerperal diseases of the breast. [Name disease.] 

(VIII. — Diseases of the Skin and Cellular Tissue) 

142. Gangrene. [State part affected, Diabetic (50), etc.] 

143. Furuncle. 

144. Acute abscess. [Name part affected, nature, or cause.] 

145. Other diseases of the skin and annexa. [Name disease.] 

^ In the sense of conditions or operations dependent upon pregnancy 
or labor, not " accidents " from external causes. 

2 In the sense of conditions or operations dependent upon pregnancy 
or labor, not " accidents " from external causes. 



PRESENT CLASSIFICATION 265 

(IX. — Diseases of the Bones and of the Organs of 
Locomotion) 

146. Diseases of the bones (tuberculosis excepted): [Name disease.] 

Osteoperiostitis, [Give cause.] 

Osteomyelitis, 

Necrosis, [Give cause.] 

Mastoiditis, etc. [Following Otitis media (76)?] 

147. Diseases of the joints (tuberculosis and rheumatism excepted). 

[Name disease; always specify Acute articular rheumatism 
(47), Arthritis deformans (48), Tuberculosis of — joint (33), 
etc., when cause is known.] 

148. Amputations. [Name disease or injury requiring amputation, 

thus permitting proper assignment elsewhere.] 

149. Other diseases of the organs of locomotion. [Name disease.) 

(X. — Malformations) 

150. Congenital malformations (stillbirths not included): [Do not 

include Acquired hydrocephalus (74) or Tuberculous hydro- 
cephalus (Tuberculous meningitis) (30) under this head.) 

Congenital hydrocephalus. 

Congenital malformation of heart, 

Spina bifida, etc. 

(XI. — Diseases of Early Infancy) 

151. Congenital debility, icterus, and sclerema: [Give cause of debility.] 

Premature birth, 

Atrophy, [Give cause.] 
Marasmus, [Give cause.] 
Inanition, etc. [Give cause.] 

152. Other diseases peculiar to early infancy: 

Umbilical hemorrhage, 

Atelectasis, 

Injury by forceps at birth, etc. 

153. Lack of care. 

(XII. — Old Age) 

154. Senility. [Name the disease causing the death of the old 

person.] 



266 CAUSES OF DEATH 

(XIII. — Affections Produced by External Causes) 

Note. — Coroners, medical examiners, and physicians who certify 
to deaths from violent causes, should always clearly indicate the funda- 
mental distinction of whether a death was due to Accident, Suicide, or 
Homicide; and then state the Means or instrument of death. The 
qualification '' 'probably " may be added when necessary. 

155. Suicide by poison. [Name poison.] 

156. Suicide by asphyxia. [Name means of death.] 

157. Suicide by hanging or strangulation. [Name means of stran- 

gulation.] 

158. Suicide by drowning. 

159. Suicide by firearms. 

160. Suicide by cutting or piercing instruments. [Name instrument.] 

161. Suicide by jumping from high places. [Name place.] 

162. Suicide by crushing. [Name means.] 

163. Other suicides. [Name means.] 

J.64. Poisoning by food. [Name kind of food.] 

165. Other acute poisonings. [Name poison; specify Accidental.] 

166. Conflagration. [State fully, as Jumped from Window of burning 

dwelling, Smothered — burning of theater, Forest fire, etc.] 

167. Bums (conflagration excepted). [Includes Scalding.] 

168. Absorption of deleterious gases (conflagration excepted) : 

Asphyxia by illuminating gas (accidental). 

Inhalation of (accidental), [Name gas.] 

Asphyxia (accidental), [Name gas.] 
Suffocation (accidental), etc. [Name gas.] 

169. Accidental drowning. 

170. Traumatism by firearms. [Specify Accidental.] 

171. Traumatism by cutting or piercing instruments. [Name instru- 

ment. Specify Accidental.] 

172. Traumatism by fall. [For example, Accidental fall from window.] 

173. Traumatism in mines and quarries: 

Fall of rock in coal mine, 

Injury by blasting, slate quarry, etc. 

174. Traumatism by machines. [Specify kind of machine, and if the 

Occupation is not fully given under that head, add sufficient to 
show the exact industrial character of the fatal injury. Thus, 
Crushed by passenger elevator; Struck by piece of emery 
wheel (knife grinder) ; Elevator accident (pile driver), etc.] 



PRESENT CLASSIFICATION 267 

175. Traumatism by other crushing: 

Railway collision, 

Struck by street car, 

Automobile accident. 

Run ove by dray, 

Crushed by earth in sewer excavation, etc. . 

176. Injuries by animals. [Name animal.] 

177. Starvation. [Not " inanition " from disease.] 

178. Excessive cold. [Freezing.] 

179. Excessive heat. [Sunstroke.] 

180. Lightning. 

181. Electricity (lightning excepted). [How? Occupational?] 

182. Homicide by firearms. 

183. Homicide by cutting or piercing instruments. [Name instru- 

ment.] 

184. Homicide by other' means. [Name means.] 

185. Fractures (cause not specified). [State means of injury. The 

nature of the lesion is necessary for hospital statistics but 
not for general mortality statistics.] 

186. Other external causes: 

Legal hanging, 
Legal electrocution. 

Accident, injury, or traumaiisml (unquaUfied) . [State Means 
of injtiry.] 



(XIV. — Ill-Defined Diseases) 

Note. — If physicians will familiarize themselves with the nature 
and purposes of the International List, and will cooperate with the 
registration authorities in giving additional information so that returns 
can be properly classified, the number of deaths compiled under this 
group will rapidly diminish, and the statistics will be more creditable 
to the office that compiles them and more useful to the medical pro- 
fession and for sanitary purposes. 

187. Ill-defined organic disease: 

Dropsy, Ascites, etc. [Name the disease of the heart, liver, 
or kidneys in which the dropsy occurred.] 

" 188. Sudden death. [Give cause. Puerperal?] 



268 CAUSES OF DEATH 

189. Cause of death not specified or ill-defined. [It may be extremely 
difl&cult or impossible to determine definitely the cause of death 
in some cases, even if a post-mortem be granted. If the physi- 
cian is absolutely unable to satisfy himself in this respect, it is 
better for him to write Unknown than merely to guess at the 
cause. It will be helpful if he can specify a little further, as 
Unknown disease (which excludes external causes) , or Unknown 
chronic disease (which excludes the acute infective diseases), 
etc. Even the ill-defined causes included under this head are 
at least useful to a limited degree, and are preferable to no 
attempt at statement. Some of the old " chronics," which 
well-informed physicians are coming less and less to use, are 
the following: Asphyxia; Asthenia; Bilious fever; Cachexia; 
Catarrhal fever; Collapse; Coma; Congestion; Cyanosis; De- 
hility ; Delirium; Dentition; Dyspnea; Exhaustion; Fever; 
Gastric fever ; HEART FAILURE; Laparotomy; Marasmus; 
Paralysis of the heart; Surgical shock; and Teething. In 
many cases so reported the physician could state the disease 
(not mere symptom or condition) causing death.] 



PRESENT CLASSIFICATION 



269 



LIST OF UNDESIRABLE TERMS 



Undesirable Term. 

(It is understood that the term 
criticised is in the exact form 
given below, without further ex- 
planation or qualification.) 



(1) 



** Abscess," " Abscess of brain," 
" Abscess of lung," etc. 



" Accident," " Injury," " External 
causes," " Violence." Also 
more specific terms, as " Drown- 
ing," " Gun-shot," which might 
be either accidental, suicidal, 
or homicidal. 

" Anasarca," " Ascites." 

" Atrophy," " Asthenia," " Debil- 
ity," " Decline," " Exhaustion," 
" Inanition," " Weakness," and 
other vague terms. 



*' Blood poisoning " . 



" Cancer," " Carcinoma," " Sar- 
coma," etc. 

" Catarrh " 



" Cardiac insufficiency," " Cardiac 
degeneration," " Cardiac weak- 
ness," etc. 

" Cardiac dilatation " 



" Cellulitis 



Cerebrospinal meningitis." 



" Congestion," '' Congestion of bow- 
els," " Congestion of the brain," 
" Congestion of kidneys," " Con- 
gestion of lungs," etc. 



Reason Why Undesirable, and Suggestion for 
More Definite Statement of Cause of Death. 



(2) 



W^s it tuberculous-or due to other infection? Trau- 
matic? The return of " Abscess," unqualified, is 
worthless. State cause (in which case the fact of 
" abscess " may be quite unimportant) and loca- 
tion. 

Impossible to classify satisfactorily. Always state 
(1) whether Accidental, Suicidal, or Homicidal; 
and (2) Means of injury {e.g.. Railroad accident). 
The lesion (e.g.. Fracture ot skull) may be added, 
but is of secondary importance for general mortal- 
ity statistics. 

See " Dropsy." 

Frequently cover tuberculosis and other' definite 
causes. Name the disease causing the condition. 



See " Septicemia." Syphilis? 

In all cases the organ or part first affected by 
cancer should be specified. 

Term best avoided, if possible. 

See " Heart disease " and " Heart failure. 



Do not report when a mere terminal condition. 
State cause. 

See " Abscess," " Septicemia." 

See " Meningitis." 

Alone, the word " congestion " is worthless, and in 
combination it is almost equally undesirable. If 
the disease amounted to inflammation, use the 
proper term (lobar pneumonia, chronic nephritis, 
enteritis, etc.); merely passive congestion should 
not be reported as a cause of death. State the 
primary cause. 



270 



CAUSES OF DEATH 



LIST OF UNDESIRABLE TERMS (Continued) 



Undesirable Term. 



(1) 



"Convulsions," "Eclampsia, 
" Fit," or " Fits." 



" Croup " . 



" Dentition," " Teething " . 



Disease," " Trouble," or " Co7n- 
plaint " of [any organ\, e.g., 
" Lung trouble," " Kidney com- 
plaint," " Disease of brain," etc. 



" Dropsy " . 



"Edema of lungs" . 



" Fever ' 



" Fracture," 
etc. 



Fracture of skull," 



" Gastritis," " Gastric 
" Acute indigestion." 



catarrh," 



Reason Why Undesirable, and Suggestion for 
More Definite Statement of Cause of Death. 



(2) 



"It is hoped that this indefinite term [" Convul- 
sions "] will henceforth be restricted to those cases 
in which the true cause of that symptom can not 
be ascertained. At present more than eleven per 
cent of the total deaths of infants under one year 
old are referred to ' convulsions ' merely." — Reg- 
istrar-General. "Fit. — This is an objectionable 
term; it is indiscriminately applied to epilepsy, 
convulsions, and apoplexy in different parts of the 
country." — Dr. Farr, in First Rep. Reg. -Gen., 1839. 

" Croup " is a most pernicious term from a public 
health point of view, is not contained in any form 
in the London or Bellevue Nomenclatures, and 
should be entirely disused. Write Diphtheria 
when this disease is the cause of death. 

State disease causing death. 

Name the disease, e.g.. Lobar pneumonia, Tuber- 
culosis of lungs. Chronic interstitial nephritis, 
Syphilitic gumma of brain, etc. 



' Dropsy ' should never be returned as the cause of 
death without particulars as to its probable origin, 
e.g., in disease of the heart, liver, kidneys, etc." — 
Registrar-General. Name the disease causing (the 
dropsy and) death. 



Usually terminal, 
condition. 



Name the disease causing the 



Name the disease, as T3rphoid fever, Lobar pneu- 
monia, Malaria, etc., in which the " fever " 
occurs. 

Indefinite; the principle of classification for general 
mortality statistics is not the lesion but (1) the 
nature of the violence that produced it (Acciden- 
tal, Suicidal, Homicidal), and (2) the Means of 
injury. 

Frequently worthless as a statement of the actual 
cause of death; the terms should not be loosely 
used to cover almost any fatal affection with irri- 
tation of stomach. Gastroenteritis? Acute or 
chronic, and cause? 



PRESENT CLASSIFICATION 



271 



LIST OF UNDESIRABLE TERMS (Continued) 



Undesirable Term 



(1) 



" General decay, etc. 



" Heart disease," " Heart trouble," 
even " Organic heart trouble." 



" Heart failure," " Cardiac weak- 
ness," " Cardiac asthenia,' 
" Cardiac exhaustion," " Paraly- 
sis of the heart, ' etc. 



Hemorrhage," " Hemoptysis," 
" Hemorrhage of lungs." 



" Hydrocephalus 



" Hysterectomy " . 



" Infantile asthenia," " Infantile 
atrophy," " Infantile debility," 
" Infantile marasmus," etc. 

" Infantile paralysis " 



"Inflammation". 
"Laparotomy " . . 



Reason Wnr Undesirable, and Suggestion for 
More Definite Statement of Cahse of Death. 



(2) 



See " Old age." 

The exact form of the cardiac affection, as Mitral 
regurgitation, Aortic stenosis., or, less precisely, 
as Valvular heart disease, should be stated. 

" Heart failure " is a recognized synonym, even 
among the laity, for ignorance of the cause of death 
on the part of the phj'sician. Such a return is for- 
bidden by law in Connecticut. If the physician 
can make no more definite statement, it must be 
compiled among the class of ill-defined diseases 
(not under Organic heart diseased 

Frequently mask tuberculosis or deaths from in- 
juries (traumatic hemorrhage), Puerperal hem- 
orrhage, or hemorrhage after operation for various 
conditions. What was the cause and location of 
the hemorrhage? If from violence, state fully 
(p. 11). 

"It is desirable that deaths from hydrocephalus of 
tuberculous origin should be definitely assigned 
in the certificate to Tuberculous meningitis, so 
as to distinguish them from deaths caused by 
simple inflammation or other disease of the brain 
or its membranes. Congenital hydrocephalus 
should always be returned as such." — Registrar- 
General. 

See " Operation." 

See "Atrophy." 



This term is sometimes used for paralysis of infants 
caused by i strumental delivery, etc. The im- 
portance of the disease in its recent endemic and 
epidemic prevalence in the United States makes 
the exact and unmistakable expressions Acute an- 
terior poliomyelitis or Infantile paralysis (acute 
anterior poliomyelitis) desirable. 

Of what organ or part of the body? Cause? 

See " Operation." 



272 



CAUSES OF DEATH 



LIST OF UNDESIRABLE TERMS (Continued) 



Undesirable Term. 



(1) 



Malignant," " Malignant dis- 
ease." 



Malnutrition". 
Marasmus" ... 



" Meningitis," " Cerebral meningi- 
tis," " Cerebrospinal meningi- 
tis," " Spinal meningitis." 



' Natural causes ' 



" Old age," " Senility," etc. 



" Operation," " Surgical opera- 
tion," " Surgical shock," " Am- 
putation," " Hysterectomy," 
" Laparotomy," etc. 



Reason Why Undesirable, and Suggestion for 
More Definite Statement of Cause of Death, 



(2) 



Should be restricted to use as qualification for neo- 
plasms; see Tumor. 

See " Atrophy." — 

This term covers a multitude of worthless returns, 
many of which could be made definite and useful 
by giving the name of the disease causing the "ma- 
rasmus " or wasting. It has been dropped ffom 
the English Nomenclature since 1885 (" Maras- 
mus, term no longer used "). The Bellevue Hos- 
pital Nomenclature also omits this term. 

Only two terms should ever be used to report deaths 
from Cerebrospinal fever, synonym. Epidemic 
cerebrospinal meningitis, and they should be 
written as above and in no other way. It matters 
not in tte use of the latter term whether the disease 
be actually epidemic or not in the locality. A 
single sporadic case should be so reported. The 
first term (Cerebrospinal fever) is preferable be- 
cause there is no apparent objection to its use for 
any number of cases. No one can intelligently 
classify such returns as are given in the margin. 
Mere terminal or symptomatic meningitis should 
not be entered at all as a cause of death; name the 
disease in which it occurred. Tuberculous men- 
ingitis should be reported as such. 

This statement eliminates external causes, but is 
otherwise of little value. What disease (prob- 
ably) caused death ? 

Too often used for deaths of elderly persons who suc- 
cumbed to a definite disease. Name the disease 
causing death. 

All these are entirely indefinite and unsatisfactory 
— unless the surgeon desires his work to be held 
primarily responsible for the death. Name the 
disease, abnormal condition, or form of 'external 
violence (Means of death; accidental, suicidal, 
or homicidal ?) , for which the operation was per- 
formed. If death was due to an anesthetic (chlo- 
« rofonn, ether, etc.), state that fact and the name 
of the anesthetic. 



PRESENT CLASSIFICATION 273 

LIST OF UNDESIRABLE TERMS (Continued) 



Undesirable Term. 



(1) 



Reason Why Undesirable, and Suggestion for 
More Definite Statement of Cause of Death. 



(2) 



Paralysis," " General paralysis," 
" Paresis," " General paresis," 
"Palsy," etc. 



Peritonitis". 



Pneumonia," " Typhoid pneu- 
monia." 



The vague use of these terms should be avoided, and 
the precise form stated, as Acute ascending paral- 
ysis, Paralysis agitans. Bulbar paralysis, etc. 
Write General paralysis of the insane in full, 
not omitting any part of the name; this is essential 
for satisfactory compilation of this cause. Distin- 
guish Paraplegia and Hemiplegia; and in the 
latter, when a sequel of Apoplexy or Cerebral 
hemorrhage, report the primary cause. 

" Whenever this condition occurs — either as a con- 
sequence of Hernia, Perforating ulcer of the 
stomach or bowel [Typhoid fever?]. Appendicitis, 
or] Metritis (puerperal or otherwise), or else 
as an extension of morbid processes from other 
organs [Name the disease], the fact should be 
mentioned in the certificate." — Registrar-General. 
Always specify Puerperal peritonitis in cases re- 
sulting from abortion, miscarriage, or labor at full 
term. Always state if due to tuberculosis or 
cancer. When traumatic, report means of injury 
and whether accidental, suicidal, or homicidal. 

" Pneumonia," without qualification, is indefirute; 

. it should be clearly stated either as Bronchopneu- 
monia or Lobar pneumonia. The term Croup- 
ous pneumonia is also clear. " The term ' Ty- 
phoid pneumonia ' should never be employed, as it 
may mean either Enteric fever [Typhoid fever] 
with pulmonary complications, on the one hand 
or Pneumonia with so-called typhoid symptoms on 
the other. ' ' — Registrar-General. When lobar pneu- 
monia or bronchopneumonia occurs in the course 
of or following a disease the primary cause should 
be entered first, with duration, and the lobar 
pneumonia or bronchopneumonia be entered be- 
neath as the contributory cause, with duration. 
Do not report " Hypostatic pneumonia " or other 
mere terminal conditions as causes of death when 
the disease causing death can be ascertained. 



274 



CAUSES OF DEATH 



LIST OF UNDESIRABLE TERMS (Continued) 



Undesirable Term. 



(1) 



Ptomain poisoning," " Autoin- 
toxication," " Toxemia," etc. 



" Pulmonary congestion," " Pul- 
monary hemorrhage." 



' Pyemia ' 



" Septicemia," " Sepsis," " Sep- 
tic infection," etc. 



*' Shock " (post-operative) . 
" Specific " 



*' Tabes mesenterica," " Tabes " ... 
} 



"Teething" 

" Toxem,ia" . . . 
" Tuberculosis " 



Reason Why Undesirable, and Suggestion fob 
More Definite Statement of Cause of Death. 



(2) 



These terms are used very loosely and it is impos- 
sible to compile statistics of value unless greater 
precision can be obtained. They should not be 
used when merely descriptive of symptoms or con- 
ditions arising in the course of diseases, but the 
disease causing death should alone be named. 
" Ptomain poisoning " should be restricted to 
deaths laaulting from the development of putre- 
factive alkaloids or other poisons in food, and the 
food should be named, as Ptomain poisoning 
(mussels), etc. 

See " Congestion," " Hemorrhage." 



See " Septicemia." 

Always state cause of this condition, and, if local- 
ized, part a£fected. Puerperal? Traumatic (see 
p. 11)? 

See " Operation." 

The word specific should never be tised without 
further explanation. It may signify syphilitic, 
tuberculous, gonorrheal, diphtheritic, etc. Name the 
disease. 

" The use of this term [" Tabes mesenterica "] to de- 
scribe tuberculous disease of the peritoneum or in- 
testines should be discontinued, as it is frequently 
used to denote various other wasting diseases 
which are not tuberculous. . Tuberculous i)erito- 
nitis is the better term to employ when the condi- 
tion is due to tubercle." — Registrar-General. 
Tabes dorsalis should not be abbreviated to 
" Tabes." 

See "Dentition." 

See " Ptomain poisoning." 

The organ or part of the body affected should always 
be stated, as Tuberculosis of the lungs, Tuber- 
culosis of the spine, Tuberculous meningitis, 
Acute general miliary tuberculosis, etc. 



SYNONYMS USED FOR "TYPHOID FEVER 



275 



LIST OF UNDESIRABLE TERMS (Concluded) 



Undesirable Term. 


Reason Why Undesirable, and Suggestion for 
More Definite Statement of Cause of Death. 


(1) 


(2) 


" Tumor," " Neoplasm," " New 
growth." 

" Uremia " 


These terms should never be used without the qual- 
fying words Malignant, Nonmalignant, or Be- 
nign. If malignant, they belong under Cancer, 
and should preferably be so reported, or under the 
more exact terms Carcinoma, Sarcoma, etc. In 
all cases the oigan or part affected should be 
specified. 

Name the disease causing death, i.e., the primary 
cause, not the mere terminal conditions or symp- 
toms, and state the duration of the primary 
cause. 

See " Hemorrhage." 


" Uterine hemorrhage " 







Some of the synonyms used for '' typhoid fever." — The 
following is a partial list of terms which have been used to 
describe typhoid fever: 



Abdominal fever, 
Abdominal typhoid, 
Abdominal typhus. 
Abortive typhoid, 
Ambulant typhoid, 
Cerebral typhoid, 
Cerebral typhus 
Continued fever, 
Enteric fever, 
Enterica, 

Gastroenteric fever 
Hgpmorrhagic typhoid fever, 
Ileotyphus, 

Intermittent typhoid fever. 
Malignant typhoid fever. 
Mountain fever. 
Paratyphoid fever. 



Paratyphus, 
Posttyphoid abscess 
Rheumatic typhoi^ fever, 
Typhobilious fever, 
Typhoenteritis, 
Typhogastric fever, 
Typhoid fever, 
Typhoid malaria. 
Typhoid meningitis, 
Typhoid stupor, 
Typhoid ulcer 
Typhomalaria, 
Typhomalarial fever, 
Typhoperitonitis, 
Typhus 
Typhus abdominaiis. 



This shows the great need of standardization. 



276 CAUSES OF DEATH 

Joint causes of death. — The Bureau of the Census in 
1914 published an " Index of Joint Causes of Death," which 
shows the proper method of assignment to the preferred 
title of causes of death when two causes are simultaneously 
reported. This index, alphabetically arranged, is very 
useful. Physicians sometimes report two or more causes 
of death upon the death-certificate. This may be histori- 
cally true as one disease may be a complication of the other. 
For statistical purposes, however, only one cause can be 
tabulated for each death. Out of the two or more causes 
given one must be selected, and it is a matter of great impor- 
tance how this is done. For some years the attempt has 
been made to separate the diseases reported into the primary 
cause and secondary cause. As this gave rise to some uncer- 
tainty as to which was which, the form of the Revised U. S. 
Standard Certificate of Death asks for ^^The Cause of Death" 
and for "The Contributory Cause (Secondary)." The Eng- 
lish, French and Germans have laid down certain rules for 
making the proper selections. In general, it may be said that 
the primary cause is the real, or underlying, cause of death 
(the primao-y affection with respect to time and causation). 
The following are the American instructions as printed on 
the back of the standard death-certificate. 

STANDARD CERTIFICATE OF DEATH 

Statement of occupation. — Precise statement of occupation is verj 
important, so that the relative healthfulness of various pursuits can be 
known. The question applies to each and every person, u-respective o\ 
age.- For many occupations a single word or term on the first line wil 
be sufficient, e.g., Farmer or Planter, Physician, Compositor, Architect 
Locomotive engineer. Civil engineer, stationary fireman, etc. But ir 
many cases, especially in industrial employments, it is necessary t( 
know (a) the kind of work and also (6) the nature of the business o] 
industry, and therefore an additional line is orovided for the latte; 
statement; it should be used only when needed. As examples: (a 



JOINT CAUSES OF DEATH 277 

Spinner, (b) Cotton mill, (a) Salesman, (6) Grocery, (a) Foreman, (6) 
Automobile factory. The material worked on may form part of the 
second statement. Never retm-n " Laborer," " Foreman," " Manager," 
" Dealer," etc., without more precise specification, as Day laborer. Farm 
laborer, Laborer — Coal mine, etc. Women at home who are engaged 
in the duties of the household only (not paid Housekeepers who receive 
a definite salary) may be entered as Housewife, Housework, or At 
home, and children, not gainfully employed, as At school or At home. 
Care should be taken to report specifically the occupations of persons 
engaged in domestic service for wages, as Servant, Cook, Housemaid, 
etc. If the occupation has been changed or given up on account of 
the Disease Causing Death, state occupation at beginning of illness. 
If retired from business, that fact may be indicated thus: Farmer 
(retired, 6 yrs.). For persons who have no occupation whatever, write 
None. 

Statement of cause of death. — Name, first, the Disease Causing 
Death (the primary affection with respect to time and causation), 
using always the same accepted term for the same disease. Examples: 
Cerebrospinal fever (the only definite synonym is " Epidemic cerebro- 
spinal meningitis"); Diphtheria (avoid use of "Croup"); Typhoid 
fever (never report " Typhoid pneumonia "); Lobar pneumonia; Bron" 
chopneumonia ("Pneumonia," unqualified, is indefinite); Tuber- 
culosis of lungs, meninges, peritoneum, etc.. Carcinoma, Sarcoma, etc., 

of (name origin: " Cancer " is less definite; avoid use of 

"jTumor" for malignant neoplasms); Measles; Whooping cough; 
Chronic valvular heart disease; Chronic interstitial nephritis, etc. The 
contributory (secondary or intercurrent) affection need not be stated 
unless important. Example: Measles (disease causing death), 29 ds.; 
Broncho-pneumonia (secondary), 10 ds. Never report mere symptoms 
or terminal conditions, such as " Asthenia," " Anemia," (merely 
symptomatic), " Atrophy," " Collapse," " Coma," " Convulsions," 
"Debility" ("Congenital," "Senile," etc.), "Dropsy," "Exhaus- 
tion," " Heart failure," " Hemorrhage," " Inanition," " Marasmus," 
" Old age," " Shock," " Uremia," " Weakness," etc., when a definite 
disease can be ascertained as the cause. Always qualify all diseases 
resulting from childbirth or miscarriage, as " Puerperal septicemia,'" 
" Puerperal peritonitis,''^ etc. State cause for which surgical operation 
was undertaken. 

For violent deaths state means of injury and qualify as acci- 
dental, SUICIDAL, or HOMICIDAL, or as probably such, if impossible to 
determine definitely. Examples : Accidental drowning; Struck by railway 



278 CAUSES OF DEATH 

train — accident; Revolver wound of head — homicide; Poisoned by carbolic 
acid — probably suicide. The nature of the injury, as fracture of skull, 
and consequences (e. g., sepsis tetanus) maybe stated under the head of 
" Contributory." (Recommendations on statement of cause of death 
approved by Committee on Nomenclature of the American Medical 
Association.) 

Cases for the Medical Examiners. — Under the provisions of chapter 
24 of the Revised Laws deaths under the following conditions must be 
referred to the Medical Examiners : 

1. Deaths following injury or violence, as Burns, Falls, Drowning, 

Gas poisoning, Suicide, Homicide, etc. 

2. Deaths supposedly caused by violence, as Criminal abortion. 

Poisoning, Starvation, Suffocation, Exposure, etc. 

3. Sudden deaths of persons not disabled by recognized disease, as 

A death upon the street, or one supposed to be due t& Alcoholism, etc. 

4. Deaths under circumstances unknown, as A person found dead, etc. 

The following supplementary suggestions are also useful.'- 
J 1 . Select the primary cause, that is, the real or under- 
lying cause of death. This is usually — 

(a) The cause first in order. 

(6) The cause of longer duration. If the physician 
writes the cause of shorter duration first, in- 
quiry may be made whether it is not a mere 
symptom, complication, or terminal condition. 

(c) The cause of which the contributory (secondary) 
cause is a frequent complication. See lists of 
'' Frequent complications " under the various 
titles of the Tabular List. 

{d) The physician may indicate the relation of the 
causes by words, although this is a departure 
from the way in which the blank was in- 
tended to be filled out. For example, 
^' Bronchopneumonia following measles '^ 
(primary cause last) or '' measles followed hy 
brochopneumonia " (primary cause first). 

1 Manual, 1911, 1, p. 23. 



JOINT CAUSES OF DEATH 279 

2. If the relation of primary and secondary is not clear, 
prefer general diseases, and especially dangerous infective 
or epidemic diseases, to local diseases. 

3. Prefer severe or usually fatal diseases to mild dis- 
eases. 

4. Disregard ill-defined causes (Class XIV), and also 
indefinite and ill-defined terms {e.g., " debility," " atro- 
phy ") in Classes XI and XII that are referred, for certain 
ages, to Class XIV, as compared with definite causes. 
Neglect mere modes of death (failure of heart or respira- 
tion) and terminal symptoms or conditions {e.g., hypostatic 
congestion of lungs). 

5. Select homicide and suicide in preference to any con- 
sequences, and severe accidental injuries, sufficient in 
themselves to cause death, to all ordinary consequences. 
Tetanus is preferred to any accidental injury and ery- 
sipelas, septicaemia, pyaemia, peritonitis, etc., are pre- 
ferred to less serious accidental injuries. Prefer definite 
means of accidental injury {e.g., railway accident, explosion 
in coal mine, etc.) to vague statements or statement of the 
nature of the injury only {e.g., accident, fracture of skull). 

6. Physical diseases {e.g., tuberculosis of lungs, diabetes) 
are preferred to mental diseases as causes of death {e.g., 
manic depressive psychosis), but general paralysis of the 
insane is a preferred term. 

7. Prefer puerperal causes except when a serious dis- 
ease {e.g., cancer, chronic Bright's disease) _ was the inde- 
pendent cause. 

8. Disregard indefinite terms and titles generally in 
favor of definite terms and titles. The precise line of 
demarcation is difficult to lay down, but may be indicated 
broadly by the kinds of type employed in the International 
List presented on page 35. The List in this form has been 
distributed by the Census to all physicians in the United 



280 CAUSES OF DEATH 

States/ so that the proportion of indefinite returns should 
become less. 

Occupation. — During recent years the study of the rela- 
tion between occupation and disease has received much 
attention, and this study has shown the very great impor- 
tance of the industrial hazard. Fundamental to such a 
study is a proper classification of occupations. The list 
which follows was published by the Bureau of the Census in 
1915. It is taken from a report entitled ''Index to Occupa- 
tions, alphabetical and classified," a book of 414 pages. 

This classification contains 215 main groups, 84 of which 
are subdivided, making a total of 428 separate groups. The 
industrial field is divided into eight general divisions, and 
each occupation has been ''classified in that part of the 
industrial field in which it is most commonly pursued. '^ 
Clerical occupations are classified apart. The classification 
is along occupational rather than industrial lines. In the 
table each occupation is indicated by a symbol consisting of 
three figures, the first of which indicates one of the following 
main divisions: 

0. Agriculture, forestry and animal husbandry, 

1. Extraction of minerals. 
2.' 

3. • Manufacturing and mechanical industries. 
4. 

5. Transportation. 

6. Trade. 

1 Public Service. 

*J Professional Service, 

8. Domestic and Personal Service. 

9. Clerical Occupations. 

^ See Physicians' Pocket Reference to the International List of 
Causes of Death. 



OCCUPATIONS 281 

The second and third figures of each symbol are used in 
combination and indicate the occupation under the given 
main division. Thus in the symbol 529, 5 stands for '' Trans- 
portation" and 29 for ''Brakeman-steam railroad." 

The report emphasizes the need of great care in distinguish- 
ing between occupations and gives the following as examples 
of distinctions which must be made : — 

An iron foundry and a brass foundry. 

A felt hat factory and a straw hat factory. 

A steam railroad and a street railway. 

A paper box and a wooden box factory. 

A locomotive engineer and a stationary engineer. 

A wholesale and a retail merchant or dealer. 

A clerk in a store and a salesman. 

A machinist and a machine tender. 

A paid housekeeper and a housewife in her own home. 

A paid housekeeper and a servant girl. 

A cook and a servant. 

A proprietor and an employee, etc. 

LIST OF OCCUPATIONS AND OCCUPATION GROUPS WITH 

THEIR SYMBOLS 

Symbol. Occupation and occupation group. 

Agriculture, Forestry, and Animal Husbandry 

1 . . . . Dairy farmers 

1 2. . . . Dairy farm laborers 

1 4. . . . Farmers^ 

Fai*!!! laborers 
2 1 . . . . Farm laborers (home farm) 
2 2. . . . Farm laborers (working out) 
2 3. . . . Turpentine farm laborers 

Farm, dairy farm, garden, orchard, etc., foremen 
2 5 . . . . Dairy farm foremen 
2 6. . . . Farm foremen ^ 
2 7 . . . . Garden and greenhouse foremen 
2 8. . . . Orchard, nursery, etc., foremen 

' Includes turpentine farmers. 2 Includes turpentine farm foremen. 



282 



CAUSES OF DEATH 



Symbol Occupation and occupation group. 

Agriculture. Forestry, and Animal Husbandry — Continued 

3 3 . , . . Fishermen and oystermen 
3 5 Foresters 

Gardeners, florists, fruit growers, and nurserymen 

4 2 Florists 

4 3 . . . . Fruit growers and nurserymen 

4 4. . . . Gardeners 

4 5 . . . . Landscape gardeners 

Garden, greenhouse, orchard, and -nursery laborers 
5 .... Cranberry bog laborers 
5 5. . . . Garden laborers 
5 6. . . . Greenhouse laborers 
5 7.... Orchard and nursery laborers 

Lumbermen, raftsmen, and woodchoppers 
6 5 . . . . Foremen and overseers 
6 6.... Lumbermen and raftsmen 
6 7 . . . . Teamsters and haulers 
6 8. . . . Woodchoppers and tie cutters 

7 5 . . . . Owners and managers of log and timber camps 
7 7 . . . . Stock herders, drovers, and feeders 
7 9 . . . . Stock raisers 

Other agricultural and animal husbandry pursuits 
8 5 . . . . Apiarists 
8 6 . . . . Corn shellers, hay balers, grain threshers, etc. 

8 7 Ditchers (farm) 

8 8 . . . . Poultry raisers and poultry yard laborers 
8 9 . . . . Other and not specified pursuits 



Extraction of Minerals 

Foremen, overseers, and inspectors 
1 . . . . Foremen and overseers 
1 1 . . . . Inspectors 

Operators, officials, and managers 
1 1 . . . . Managers 

1 1 1 Officials 

1 1 2 . . . . Operators 



OCCUPATIONS 



283 



Symbol. 



1 2 2. 
1 3 3. 
1 4 4. 
1 5 5. 



Occuoation and occupation group. 

Extraction of Minerals — Continued 

Coal mine operatives 
Copper mine operatives 
Gold and silver mine operatives 
Iron mine operatives 



Operatives in other and not specified mines 

1 6 6 Lead and zinc mine operatives 

1 6 7 All other mine operatives 

1 7 7. . . . Quarry operatives 

Oil, gas, and salt well operatives 
1 8 8 Oil and gas well operatives 

1 8 9 Salt well and works operatives 

Manufacturing and Mechanical Industries 

Apprentices 

2 ' Apprentices to building and hand trades 

2 1 Dressmakers' and milliners' apprentices 

2 2 Other apprentices 

2 1 Bakers 



2 11 
2 12, 



1 6. 
1 7. 
1 8. 



2 2 4. 
2 2 5. 



Blacksmiths, forgemen, and hammermen 
Blacksmiths 
Forgemen, hammermen, and welders 

Boiler makers 

Brick and stone masons 

Builders and building contractors 

Butchers and dressers (slaughterhouse) 

Cabinetmakers 

Carpenters 

Compositors, linotypers, and typesetters 

Coopers 

Dressmakers and seamstresses (not in factory) 

Dyers 

Electricians and electrical engineers 

Electrotypers, stereotypers, and lithographers 
Electrotypers and stereotypers 
Lithographers 



284 CAUSES OF DEATH 

Symbol. Occupation and occupation group. 

Manufacturing and Mechanical Industries — Continued 

2 2 6. . . . Engineers (mechanical) 
2 2 7 . . . . Engineers (stationary) 
2 2 8. . . . Engravers 

Filers, grinders, buffers, and polishers (metal) 

2 3 Buffers and polishers 

2 3 1 Filers 

2 3 2 Grinders 

2-3 3 . . . . Firemen (except locomotive and fire department) 
2 3 4. . . . Foremen and overseers (manufacturing) 



2 3 5. 
2.3 6. 
2 3 7. 
2 3 8. 

2 3 9. 



Furnace men, smelter men, heaters, pourers. etc. 
Furnace men and smelter men 
Heaters 

Ladlers and pourers 
Puddlers 

Glass blowers 



Jewelers, watchmakers, goldsmiths, and silversmiths 
2 4 . . . . Goldsmiths and silversmiths 
2 4 1 . . . . Jeweler.i and lapidaries (factory) 
2 4 2.... Jewelers and watchmakers (not in factory) 

Laborers (n. o. s.^) 

Building and hand trades 
2 4 3 . . . . General and not specified laborers 

2 4 4 . , . . Helpers in building and hand trades 

Chemical industries 
2 4 5 . . . . Fertilizer factories 

2 4 6. . . , Paint factories 

2 4 7.... Powder, cartridge, fireworks, etc., factories 

2 4 8. . . . Other chemical factories 

Clay, glass, and stone industries 
2 5 . . . . Brick, tile, and terra-cotta factories 

2 5 1 . . . . Glass factories 

2 5 2. . , . Lime, cement, and gypsum factories 

2 5 3 . . . . Marble and stone yards 

2 5 4 Potteries 

1 Not otherwise specified. 



OCCUPATIONS 



285 



Symbol. 



2 5 5. 

2 5 6. 

2 5 7. 

2 5 8. 

2 5 9. 

2 6 3. 

2 6 4. 

2 6 5. 

2 6 6. 

2 6 7. 



2 8 0. 
2 8 1. 

2 8 2. 
2 8 3. 

2 8 4. 



9 0. 
9 1. 



9 6. 

9 7. 



Occupation and occupation group. 

Manufacturing and Mechanical Industries — Continued 

Iron and steel industries 
Automobile factories 
Blast furnaces and rolling mills ^ 
Car and railroad shops 
Wagon and carriage factories 
Other iron and steel works 

Other metal industries 
3rass mills 
Copper factories 
Lead and zinc factories 
Tinware and enamelware factories 
Other metal factories 

Lumber and furniture industries 

Furniture, piano, and organ factories 
Saw and planing mills ^ 
Other woodworking factories 

Textile industries 
Cotton mills 
Silk mills 

Woolen and worsted mills 
Other textile mills 

Other industries , 

Charcoal and coke works 
Cigar and tobacco factories 
Clothing industries 
Electric light and power plants 
Electrical supply factories 
Food industries — 

Bakeries 

Butter and cheese factories 

Fish curing and packing 

Flour and grain mills 

Fruit and vegetable canning, etc. 

Slaughter and packing houses 

Sugar factories and refineries 

Other food factories 
1 Includes tinpiate mills. " Includes wooden box factories. 



286 



CAUSES OF DEATH 



Symbol. Occupation and occupation group. 

Manufacturing and Mechanical Industries — Continued 



0. 
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 



3 1 0. 

3 1 1. 

311 2. 

3 13. 

3 14. 
3 15. 

3 16. 
3 17. 
3 1 8. 

3 2 0. 
3 2 1. 



3 2 6. 



Gas works 

Liquor and beverage industries 

Oil refineries 

Paper and pulp mills 

Printing and publishing 

Rubber factories 

Shoe factories 

Tanneries ^ 

Turpentine distilleries 

Other factories 

Loom fixers 

Machinists, millwrights, and toolmakers 

Machinists and millwrights 
. Toolmakers and die setters and sinkers 

Managers and superintendents (manufacturing) 

Manufacturers and officials 
Manufacturers 
Officials 

Mechanics (n. o. s.^) 

Gunsmiths, locksmiths, and bellhangers 

Wheelwrights 

Other mechanics 

Millers (grain, flour, feed, etc.) 
Milliners and millinery dealers 

Molders, founders, and casters (metal) 
Brass molders, founders, and casters 
Iron molders, founders, and casters 
Other molders, founders, and casters 

Oilers of machinery 

Painters, glaziers, varnishers, enamelers, etc. 
Enamelers, lacquerers, and japanners 
Painters, glaziers, and varnishers (building) 
Painters, glaziers, and varnishers (factory) 



1 Not otherwise specified. 



OCCUPATIONS 



287 



'mbol. Occupation and occupation group. 

Manufacturing and Mechanical Industries — (Continued) 

3 . . . . Paper hangers 

3 1 . . . . Pattern and model makers 

3 2. . . . Plasterers 

3 3 . . . . Plumbers and gas and steam fitters 

3 4. . . . Pressmen (printing) 

3 5 . . . . RoUers and roll hands (metal) 

3 6. . . . Roofers and slaters 

3 7 . . . . Sawj^ers 

Semiskilled operatives (n. o. s.^) 
Chemical industries 
3 4 0. . . . Paint factories 

3 '4 1 . . . . Powder, cartridge, fireworks, etc., factories 

3 4 2. . . . Other chemical factories 

3 4 4. . . . Cigar and tobacco factories 

Clay, glass, and stone industries 
Brick, tile, and terra-cotta factories 
Glass factories 

Lime, cement, and gypsum factories 
Marble and stone yards 
Potteries 

Clothing industries 
Hat factories (felt) 

Suit, coat, cloak, and overall factories 
Other clothing factories 

Food industries 
Bakeries 

Butter and cheese factories 
Candy factories 
Flour and grain mills 
Fruit and vegetable canning, etc. 
Slaughter and packing houses 
Other food factories 

Harness and saddle industries 

1 Not otherwise specified. 



4 5.... 


4 6.... 


4 7.... 


4 8.... 


4 9.... 


5 5.... 


5 6.... 


5 7.... 


6 0.... 


6 1.... 


6 2.... 


6 3.... 


6 4.... 


6 5.... 


6 6.... 


6 9.... 



288 



CAUSES OF DEATH. 



Symbol. Occupation and occupation group. 

Manufacturing and Mechanical Industries — (Continued) 
Iron and steel industries 

3 7 Automobile factories 

3 7 1 . . .* . Blast furnaces and rolling miUs ^ 

3 7 2 . . . . Car and railroad shops ^ 

3 7 3 . . . . Wagon and carriage factories 

3 7 4. . . . Other iron and steel works 

Other metal industries 

3 8 0.... Brass mills 

3 8 1 . . . . Clock and watch factories 

3 8 2..,. Gold and silver and jewelry factories 

3 8 3 . , , . Lead and zinc factories 

3 8 4, . , . Tinware and enamelware factories 

3 8 5.... Other metal factories 

Liquor and beverage industries 
3 9 0. . . . Breweries 

3 9 1 . . , . Distilleries 

3 9 2, . . . Other liquor and beverage factories 

Lumber and furniture industries 
3 9 4 . . . . FiuTiiture, piano, and organ factories 

3 9 5.... Saw and planing miUs ^ 

3 9 6 . . . . Other woodworking factories 

4 . . . . Paper and pulp mills 

4 1 . . . . Printing and publishing 
4 2 . , . . Shoe factories 
4 3. . . , Tanneries 

Textile industries — 

Beamers, warpers, and slashers 
4 5 . . . . Cotton mills 

4 6.... SHk mills 

4 7 . . . . Woolen and worsted mills 

4 8. . , . Other textile mills 

Bobbin boys, doffers, and carriers 

4 1 Cotton mills 

4 11.... Silk mills 

4 1 2 . . . . Woolen and worsted miUs 

4 1 3 . . . . Other textile mills 



Includes tinplate mills. 



2 Includes car repairers for street and steam railroads. 
Includes wooden box factories. 



OCCUPATIONS 289 

Symbol. Occupation and occupation group. 

Manufacturing and Mechanical Industries — (Continued) 

Carders, combers, and lappers 
4 1 5 . . . . Cotton mills 

4 16 Silk mills 

4 1 7 . . . . Woolen and worsted mills 

4 1 8 . . . . Other textile mills 

Drawers, rovers, and twisters 
4 2 . . . . Cotton mills 

4 2 1 Silk mills 

4 2 2 . . . . Woolen and worsted mills 

4 2 3 Other textile mills 

Spinners 
4 2 5 . . . . Cotton mills 

4 2 6 Silk mills 

4 2 7 . . . . Woolen and worsted mills 

4 2 8 Other textile mills 

Weavers 

4 3 Cotton mills 

4 3 1.... Silk mills 

4 3 2.... Woolen and worsted mills 

4 3 3 Other textile mills 

Winders, reelers, and spoolers 

4 3 5 Cotton mills 

4 3 6.... Silk mills 

4 3 7 . . . . Woolen and worsted mills 

4 3 8 Other textile mills 

Other occupations 

4 4 Cotton mills 

4 4 1.... Silk mills 

4 4 2 . . . . Woolen and worsted mills 

4 4 3 Other textile mills 

Other industries 
4 6 0. . . . Electrical supply factories 

4 6 1 . . . . Paper box factories 

4 6 2 . . . . Rubber factories 

4 6 3 . . . , Other factories 



290 



CAUSES OF DEATH 



Symbol. Occupation and occupation group. 

Manufacturing and Mechanical Industries — (Continued) 

Sewers and sewing machine operators (factory) ^ 
Shoemakers and cobblers (not in factory) 

Skilled occupations (n. o. s.^) 
Annealers and temperers (metal) 
Piano and organ tuners 
Wood carvers 
Other skilled occupations 

Stonecutters 

Structural iron workers (building) 

Tailors and tailoresses 

Tinsmiths and coppersmiths 
Coppersmiths 
Tinsmiths 

Upholsterers 

Transportation 

Water transportation (selected occupations) 

Boatmen, canal men, and lock keepers 

Captains, masters, mates, and pilots 

Longshoremen and stevedores 

Sailors and deck hands 
Road and street transportation (selected occupations) 

Carriage and hack drivers 

Chauffeurs 

Draymen, teamsters, and expressmen ^ 

Foremen of livery and transfer companies 

Garage keepers and managers 

Hostlers and stable hands 

Livery stable keepers and managers 

Proprietors and managers of transfer companies 

Railroad transportation (selected occupations) 
Baggagemen and freight agents 
Baggagemen 
Freight agents 

1 Includes sewers and sewing machine operators in all factories except shoe and harness 
factories, and sack sewers in fertilizer, salt, and sugar factories, and cement, flour, and 
grain mills. 

2 Not otherwise specified. 

3 Teamsters in agriculture, forestry, and the extraction of minerals are classified with 
the other workers in those industries, respectively; and drivers for bakeries and laundries 
are classified with deliverymen in trade. 



4 7 0.... 


4 7 1.... 


4 7 2.... 


4 7 3.... 


4 7 4.... 


4 7 5.... 


4 8 0.... 


4 8 1.... 


4 8 2..;. 


4 8 3.... 


4 8 4.... 


4 8 5.... 


5 0.... 


5 2... 


5 4.... 


5 6.... 


5 8.... 


5 10.... 


5 12.... 


5 14.... 


5 16.... 


5 18.... 


5 2 0.... 


5 2 2.... 


5 2 4...-. 


5 2 5.... 



OCCUPATIONS 



291 



5 2 7. 
5 2 9. 
5 3 0. 
5 3 2. 
5 3 4. 



5 4 7. 
5 4 8. 
5 4 9. 

5 5 0. 



5 2. 



4. 
5. 

7. 
9. 



6 0. 
6 2. 
6 4. 



5 6 6. 
5 6 7. 
5 6 8. 
5 6 9. 



Occupation and occupation group. 

Transportation — (Continued) 

Boiler washers and engine hostlers 

Brakemen 

Conductors (steam railroad) 

Conductors (street railroad) 

Foremen and overseers 

Laborers 

Steam railroad 
Street railroad 

Locomotive engineers 
Locomotive firemen 
Motormen 

Officials and superintendents 
Steam railroad 
Street railroad 

Switchmen, flagmen, and yardmen 

Switchmen and flagmen (steam railroad) 
Switchmen and flagmen (street railroad) 
Yardmen (steam railroad) 

Ticket and station agents 
Express, post, telegraph, and telephone (selected oc- 
cupations) 
Agents (express companies) 

Express messengers and railway mail clerks 

Express messengers 

Railway mail clerks 
Mail carriers 

Telegraph and telephone linemen 
Telegraph messengers 
Telegraph operators 
Telephone operators 
Other transportation pursuits 
Foremen and overseers (n. o. s.^) 

Road and street building and repairing 

Telegraph and telephone companies 

Water transportation 

Other transportation 

1 Not otherwise specified. 



292 CAUSES OF DEATH 

Symbol. Occupation and occupation group. 

Transportation — (Continued) 

Inspectors 
5 7 0. . . . Steam railroad 

5 7 1 Street railroad 

5 7 2 Other transportation 

Laborers (n o. s.^) 

5 7 5 Road and street building and repairing 

5 7 6 . . . . Street cleaning 

5 7 7.... Other transportation 

Proprietors, officials, and managers (n. o. s.^) 
5 8 0.... Telegraph and telephone companies 

5 8 1 . . . . Other transportation 

Other occupations (semiskilled) 
5 8 5 . . . . Steam railroad 

5 8 6. . . . Street railroad 

5 8 7 . . . . Other transportation 



Trade 

Bankers, brokers, and money lenders 

6 . . . . Bankers and bank officials 

6 1 . . . . Commercial brokers and commission men 

6 2 . . . . Loan brokers and loan company officials 

6 3. . . . Pawnbrokers 

6 4. . . . Stockbrokers 

6 5 . . . . Brokers not specified and promoters 

6 1 1 . . . . Clerks in stores 

6 1 3 . . . . Commercial travelers 

6 1 5 . . . . Decorators, drapers, and window dressers 

Deliverymen 
6 2 . . . . Bakeries and laundries 
6 2 2 Stores 

Floorwalkers, foremen, and overseers 
6 2 4 . . . . Floorwalkers and foremen in stores 
6 2 5 . . . . Foremen, warehouses, stockyards, etc. 

1 Not otherwise specified. 



OCCUPATIONS 



293 



Occupation and occupation group. 

Trade — (Continued) 

Inspectors, gangers, and samplers 

Insurance agents and officials 
Insurance agents 
Officials of insurance companies 

Laborers in coal and lumberyards, warehouses, etc.. 
3 . , . . Coal yards 
4. . . . Elevators 
5. . . . Lumberyards 
6. . . . Stockyards 
7 . . . . Warehouses 

Laborers, porters, and helpers in stores 
Newsboys 

Proprietors, officials, and managers (n. o. s.^) 
Employment office keepers 
Proprietors, etc., elevators 
Proprietors, etc., warehouses 
Other proprietors, officials, and managers 

Real estate agents and officials 
Retail dealers 

Salesmen and saleswomen 
Auctioneers 
Demonstrators 
Sales agents 
Salesmen and saleswomen (stores) 

Undertakers 

Wholesale dealers, importers, and exporters 

Other pursuits (semiskilled) 
Fruit graders and packers 
Meat cutters 
Other occupations 

^ Not otherwise specified. 



294 


CAUSES OF DEATH 


Symbol. 


Occupation and occupation group. 


^ 


Public Service (not Elsewhere Classified) 


7 0... 


. Firemen (fire department) 


7 2... 


. Guards, watchmen, and doorkeepers 




Laborers (public service) 


7 6... 


Garbage men and scavengers 


7 7... 


Other laborers 




Marshals, sheriffs, detectives, etc. 


7 10... 


Detectives 


7 11... 


Marshals and constables 


7 12... 


Probation and truant officers 


7 13... 


Sheriffs 




Officials and inspectors (city and county) 


7 15... 


Officials and inspectors (city) 


7 16... 


Officials and inspectors (county) 




Officials and inspectors (state and United States) 


7 2 0... 


Officials and inspectors (state) 


7 2 1... 


Officials and inspectors (United States) 


7 2 5... 


. Policemen 


7 2 7... 


. Soldiers, sailors, and marines 




Other pursuits 


7 3 0... 


Life-savers 


7 3 1... 


Lighthouse keepers 


7 3 2... 


Other occupations 




Professional Service 


7 4 0... 


, Actors 


7 4 2... 


. Architects 


7 4 4... 


. Artists, sculptors, and teachers of art 




Authors, editors, and reporters 


7 4 6... 


Authors 


7 4 7... 


Editors and reporters 


7 5 0... 


Chemists, assayers, and metallurgists 




Civil and mining engineers and surveyors 


7 5 2... 


Civil engineers and surveyors 


7 5 3.. 


Mining engineers 


7 5 5... 


Clergymen 


7 5 7... 


College presidents and professors 


7 5 9... 


Dentists 



OCCUPATIONS 

Occupation and occupation group. 

Professional Service — (Continued) 

Designers, draftsmen, and inventors 

Designers 

Draftsmen 

Inventors 
Lawyers, judges, and justices 
Musicians and teachers of music 
Photographers 
Physicians and surgeons 
Showmen 

Teachers 

Teachers (athletics, dancing, etc.) 
Teachers (school) 

Trained nurses • 
Veterinary surgeons 
Other professional pursuits 

Semiprofessional pursuits 

Abstractors, notaries, and justices of peace 
Fortune tellers, hypnotists, spiritualists, etc. 
Healers (except physicians and surgeons) 
Keepers of charitable and penal institutions 
Officials of lodges, societies, etc. 
Religious and charity workers 
Theatrical owners, managers, and oflBcials 
Other occupations 
Attendants and helpers (professional service) 

Domestic and Personal Service 

Barbers, hairdressers, and manicurists 
Bartenders 

Billiard room, dance hall, skating rink, etc., keepers 
Billiard and pool room keepers 
Dance hall, skating rink, etc., keepers 

Boarding and lodging house keepers 

Bootblacks "* 

Charwomen and cleaners 

Elevator tenders 

Hotel keepers and managers 



295 



296 



CAUSES OF DEATH 



Symbol. 



8 3 
8 3 

8 4 
8 4 
8 4 6. 

8 4 8. 



5 4. 

5 5. 

6 6. 

6 8. 

7 0. 

7 3. 
7 4. 
7 5. 

7 6. 

7 7. 



8 9 5. 
8 9 6. 
8 9 7. 
8 9 8. 
8 9 9. 



9 


5 5.... 


9 


5 6.... 


9 5 7.... 


9 


6 6.... 


9 


7 6.... 


9 


7 7.... 


9 


8 7.... 


9 


8 8.... 


9 


9 9 



Occupation and occupation group. 

Domestic and Personal Service — (Continued) 

Housekeepers and stewards 

Janitors and sextons 

Laborers (domestic and professional service) 

Launderers and laundresses (not in laundry) 

Laundry operatives 

Laundry owners, officials, and managers 

Midwives and nurses (not trained) 
Midwives 
Nurses (not trained) 

Porters (except in stores) 

Restaurant, cafe, and lunch room keepers 

Saloon keepers 

Servants 

Bell boys, chore boys, etc. " 

Chambermaids 

Coachmen and footmen 

Cooks 

Other servants 

Waiters 

Other pursuits 

Bathouse keepers and attendants 
Cemetery keepers 

Cleaners and renovators (clothing, etc.) 
Umbrella menders and scissors grinders 
Other occupations 

Clerical Occupations 

Agents, canvassers, and collectors 
Agents 
Canvassers 
Collectors 
Bookkeepers, cashiers, and accountants 

Clerks (except clerks in stores) 
Shipping clerks 
Other clerks 

Messenger, bundle, and office boys ^ 
Bundle and cash boys and girls 
Messenger, errand, and office boys 
Stenographers and typewriters 

1 Except telegraph and telephone messengers. 



EXERCISES AND QUESTIONS 297 

Nosology not an exact science. — The following reported 
causes of death will enable the student to decide whether 
or not nosology is an exact science: 

"Went to bed feeling well, but woke up dead." 
"Died suddenly at the age of 103. To this time he bid fair to reach 
a ripe old age." 

"Deceased had never been fatally sick." 

"Last illness caused by chronic rheumatism, but was cured before 
death." 

"Died suddenly, nothing serious." 

"While cranking his automobile sustained what is technically known 
as a colles fracture of the right rib." 
"Kick by horse showed on left kidney." 

"Chronic disease." 

"Deceased died from blood poison caused by a broken ankle, which 
is remarkable, as the automobile struck him between the lamp and the 
radiator." 
, "Death caused by five doctors." 

"Delicate from birth." 

"Artery lung busted." 

" Collocinphantum . " 

"Typhoid fever, bronchitis, pneumonia and a miscarriage." 
— " Vital Statistics." ♦ 

EXERCISES AND QUESTIONS 

1. What does Van Buren mean by the "Will-o'-the-wisp" of the 
statistics of causes of death? [See Am. J. P. H., Dec. 1917, p. 1016.] 

2. What changes have taken place in the nomenclature of "Tuber- 
culosis," during the last century? 

3. Give ten examples of joint causes of death, indicating in each 
case which is primary and which secondary. 

4. What preparations are being made to revise the present Inter- 
national List of Causes of Death? 

5. Select the appropriate cause of death for statistical report from 
the following joint causes of death, and give reason for your selection. 

a. Broncho-pneumonia and measles. 
h. Infantile diarrhoea and convulsions, 
c. Scarlet fever and diphtheria. 



298 CAUSES OF DEATH 

d. Nephritis and scarlet fever. 

e. Pulmonary tuberculosis and puerperal septicemia. 
/. Typhoid fever and pneumonia. 

g. Pericarditis and appendicitis. 

h. Cirrhosis and angina pectoris. 

i. Saturnism and peritonitis. 

J. Old age and bronchitis. 



CHAPTER IX 
ANALYSIS OF DEATH-RATES 

Reasons for Analyzing a Death-rate. — We have now 
covered the principal methods used in the simpler forms of 
statistical study. We have seen the futility of using general 
death-rates for comparing the mortality of different places. 
We have learned how to compute specific rates for groups 
and classes, particular rates for different diseases and special 
rates of various kinds. Let us now put these ideas together 
and say that the way to use a general death-rate is to analyze 
it. Taken by itself it means very little, but if properly 
analyzed it will yield us useful information. 

Two Methods of Analysis. — There are two methods of 
analyzing a general death-rate. 

One is to sub-divide the numerator of the fraction into 
classes and groups, leaving the denominator of the fraction 
unchanged. The total population at mid-year is taken as 
the denominator of the fraction. This is sometimes done in 
separating all of the deaths in a year according to months 
and dividing each by the total population. It has the ad- 
vantage that the sum of all the parts is equal to the whole. 
In the case mentioned the sum of all the monthly rates gives 
the yearly rate. It has the disadvantage that the figures 
cannot be compared or any standard easily carried in the 
mind. 

Another and better method is to sub-divide both the 
numerator and denominator into classes and groups, that is, 
to find their specific rates. Here the sum of the rates 

299 



300 



ANALYSIS OF DEATH-RATES 



resulting from the separation does not equal the whole. The 
weighted average of the constituent rates will, however, 
equal the whole. 

Let us take a simple example: 

In 1910 in Massachusetts there were the following popu- 
lations and deaths classified by sex. 



TABLE 72 
POPULATION AND DEATHS: MASSACHUSETTS 





Population. 


Deaths. 


(1) 


(2) 


(3) 


Males 


1,655,248 
1,711,168 


28,259 


Females 


26,148 








Total 


3,366,416 


54,407 







According to the first method of analysis the partial rates 
would be 28,259 -^ 3366 = 8.4 for males, and 26,148 ^ 
3366 = 7.7 for females, the sum being 16.1, which is the 
same as dividing 54,407 by 3366, i.e., 16.1 per 1000. 

According to the second method the specific rate for males 
is 28,259 -^ 1655 = 17.1, and for females, 26,148 ^ 1711 = 
15.3. In this case the weighted average would be (17.1 X 
1655 + 15.3 X 1711) -^ 3366 = 16.1 per 1000. The ad- 
vantage of this second method is obvious, as one may readily 
compare the rate of 17.1 for males, and that of 15.3 for 
females, with 16.1, the death-rate for the entire popula- 
tion. In other words, this method of analysis gives us a 
chance to compare, and that is a prime object of statistical 
study. 

Useful subdivisions. — For the purpose of analyzing a 
general death-rate we may subdivide the area geographically, 
finding the specific death-rate for each part. A state may 



ANALYSIS OF A DEATH-RATE FOR A STATE 301 

be subdivided into counties, boroughs, cities and towns; or 
into urban and rural districts. A large city may be divided 
into wards, precincts or blocks. The subdivisions must be 
so chosen that both the population and the deaths may be 
obtained for each one. This often limits the comparison to 
political subdivisions. Those who take the census and those 
who keep the death records should get together and see that 
the geographical subdivisions correspond. Having made 
these subdivisions and obtained the rates for each, the results 
should be arrayed and studied by the statistical method 
described in a later chapter. 

We may subdivide the year into seasons, months, weeks, or 
even days and ascertain the specific death-rate for each sub- 
division. These results should be arranged for chronological 
study, and for comparing the results for similar seasons or 
months for different years. 

We may subdivide the population by sex, by nationality, 
by occupation, and in all sorts of ways. 

We may subdivide the deaths according to cause, using 
either individual causes or classes of causes. 

And finally we may use these various separations in com- 
bination with each other. 

Example of the analysis of a general death-rate for a 
state. — To give a complete example of an analysis of the 
general death-rate of a state would require a small volume. 
A few hints may be given by asking a number of questions 
in regard to Massachusetts for the year 1910. 

According to the 73d Registration Report the general 
death-rate for the state was 16.1. 

Q. Was the death-rate uniform throughout the state? 

The answer is obtained by finding the rate for each county 
and placing them in array, that is, in order of magnitude. 
The result is as follows: 



302 



ANALYSIS OF DEATH-RATES 



TABLE 73 
DEATH-RATES BY COUNTIES: MASSACHUSETTS, 1910 



County. 


General death- 
rate. 


County. 


General death- 
rate. 


(1) 


(2) 


(1) 


(2) 


Norfolk 


13.3 
14.2 
15.4 
15.5 
15.6 
15.6 
15.7 


Essex 


15.9 


Plymouth 


Bristol 


16.3 


Middlesex 


Hampden 


16.8 


Franklin 


Suffolk 


17.0 


Worcester . 

Berkshire 


Barnstable 

Dukes 


18.1 
19.1 


Hampshire 


Nantucket 


20.2 



Q. What was the median death-rate for the different 
counties, that is, the rate for the county in the middle of the 
Hst? 

It was 15.8, i.e., between 15.7 and 15.9. 

Q. Why is this median rate lower than 16.1, the rate for 
the entire state? 

The more populous counties have death-rates relatively 
high and this brings up the average. An average of these 
county rates weighted according to their popul^ion would 
give 16.1. 

Q. Why was the rate for Nantucket county so much 
higher than that for Norfolk? ; 

In order to answer this question intelligently we need to 
find out when the deaths occurred (seasonal distribution), 
where the deaths occurred (geographical distribution), who 
died (distribution by sex, age, nationality), what was the 
cause of death. Knowing these facts we should then seek 
to correlate them with controllable conditions. 

As a rule a county is not a good geographical unit for 
such a study as it is difficult to get the facts. A city is 
better. 



COMPARISON OF DEATH-RATES OF TWO CITIES 303 

Comparison of the death-rates of two cities. — In 1910 
the general death-rates of the cities of Massachusetts which 
had populations exceeding 50,000 were as follows: 



TABLE 74 

DEATH-RATES OF CERTAIN CITIES IN MASSACHUSETTS 

1910 



City. 


General death- 
rate. 


City. 


General death- 
rate. 


(1) 


(2) 


(1) 


(2) 


Brockton 


12.3 
13.1 
13.4 
15.0 
16.6 
16.9 


Boston 

Holyoke 

Lawrence 


17.2 


Lynn 

Somerville 


17.7 
17.7 


Cambridge 


Fall River 


18.4 


Springfield 


New Bedford 

Lowell 


18.6 


Worcester 


19.7 








Q. Why was the 
in Brockton ? 

We naturally lo 
tribution. The U 
mation : 


) death-rate 

ok first to c 
. S. Census 


SO much higher in Lowell than 

lifferences in age and sex dis- 
gives us the following infor- 



TABLE 75 

AGE AND SEX DISTRIBUTION OF POPULATION IN 
BROCKTON AND LOWELL, MASS. 





Brockton. 


Lowell. 


(1) 


(2) 


(3) 


Per cent of population under 10 years 
Male 


8.8 
8.6 

10.1 
10.6 


9.3 


Female 


9.3 


Per cent of population over 45 years 
Male 


9.2 


Female 


10.8 







304 ANALYSIS OF DEATH-RATES 

■ These differences are not striking, except that Lowell has 
a somewhat larger percentage of children under ten years of 
age. How about infants? There is not much difference. 
In Brockton the infant population was 2.15 per cent of the 
totalj in Lowell, 2.19 per cent. The sex differences are not 
great except that in LoT^^ell in the age-group 15-44 years 
there are more females than males, while in Brockton the 
numbers are about alike. 

Let us next turn to nationality. Here we find a great 
difference. In Brockton, 72 per cent of the population were 
native white and 27 per cent foreign-born white, but in 
Lowell only 59 per cent were native white while 40 per cent 
were foreign-born white. Pursuing this further we find that 
in Lowell the foreign-born whites were made up of French 
Canadians, 28.3 per cent; Irish, 23.0 per cent; English, 10.5 
per cent; Canadians other than French, 9.3 per cent; Greeks, 
8.7 per cent. The corresponding figures for Brockton are 
not given in the census report. 

With these fundamental differences in mind we must next 
turn to industrial conditions, living conditions, etc. Brock- 
ton is a shoe city, Lowell a textile city. The housing condi- 
tions of the working classes in Brockton are better than ir 
Lowell. These matters should be studied in detail. 

But what of the causes of death? The annual report oj 
the State Board of Health shows that the death-rate for pneu- 
monia was 118 per 100,000 in Brockton, but 210 in Lowell 
tuberculosis 88 and 137 respectively, diarrhea and cholera 
morbus 23 and 184. This last is a very important difference. 

Turning to the age distribution of deaths we find that in 
Brockton 18.5 per cent of the deaths were infants, in Lowell 
25.2 per cent. Evidently the large number of infant deaths, 
the large numbers of deaths from dysentery and the large 
foreign population in Lowell point to certain environments 
conditions which influence mortality. 



"RATES" NOT THE ONLY METHOD OF COMPARISON 305 

In order to get these facts it was necessary to consult the 
State Registration Report, the Annual Report of the State 
Board of Health and the Census Report. The annual 
reports of the local boards of health should have contained 
these essential data; in fact they should have contained the 
following specific death-rates for 1910: 



TABLE 76 

SPECIFIC DEATH-RATES BY AGE-GROUPS FOR BROCKTON 

AND LOWELL: 1910 





Specific death-rates per 1000. 


Age-group. 


Brockton. 


Lowell. 




Male. 


Female. 


Male. 


Female. 


(1) 


(2) 


(3) 


(4) 


(5) 


0-1 


123.0 


101.0 


286.0 


237.0 


1-4 


8.0 


13.0 


31.0 


35.0 


5-9 


3.5 


6.5 


5.2 


4.6 


10-14 


2.1 


3.0 


1.6 


2.7 


15-19 


4.0 


3.2 


4.7 


3.1 


20-24 


3.1 


2.6 


5.2 


5.0 


25-34 


3.9 


6.0 


7.5 


6.8 . 


35-44 


4.7 


4.3 


9.8 


10.7 


45-64 


18.4 


11.8 


24.0 


23.0 


65- 


106.0 


90.0 


99.0 


95.0 



These figures show directly that the infant death-rate was 
much higher in Lowell than in Brockton, that the death-rate 
for young children was also higher. This would point at 
once to home environment. But the rates were also higher 
in Lowell for the middle-age groups, which would point to 
greater industrial hazards there. 

*' Rates " not the only method of comparison. — So 
much has been said about rates and specific rates that there 
is danger that the student may come to think of them as 



306 



ANALYSIS OF DEATH-RATES 



the only method of statistical comparison. That is far from 
being the case. 

The seasonal changes in mortality may be shown in three 
ways, each of which has its use. In Massachusetts the 
general death-rate for 1910 was 16.1 per 1000. It varied 
seasonally as follows: 



TABLE 77 
SEASONAL DISTRIBUTION OF MORTALITY 

Massachusetts, 1910 



Month. 



(1) 



January. . 
February. 
March... . 

April 

May...'... , 

June 

July 

August ... 
September 
October . . , 
November 
December. 
Year . . 



Death-rate. 



(2) 



17.1 
17.1 
17.8 
17.2 
15.2 
14.4 
17.2 
16.6 
15.8 
14.7 
14.8 
16.2 



16.1 



Percentage of 
total deaths. 



(3) 



8.9 
8.1 
9.5 
8.8 
8.0 
7.3 
9.0 
8.7 
8.0 
7.7 
7.5 
8.5 



100.0 



Ratio of monthly 

deaths to average 

number for each 

month. 



(4) 



106 

106 

110 

107 

94 

89 

107 

103 

98 

91 

92 

101 



100 



Column (2) gives the death-rate for each month as compared 
with the yearly rate. Columns (3) and (4) are most useful 
in comparing one year with another. They do not involve 
population, an uncertain factor in all but the census years, 
but on the other hand a change in one month affects the 
figures in all the other months. 



EXERCISES AND QUESTIONS 307 

EXERCISES AND QUESTIONS 

1. Make a statistical analysis of the general death-rates of Boston 
and Baltimore for the year 1910. 

2. Make a statistical analysis of the general death-rates of Chicago 
and New Orleans for the year 1910. 

3. Make a statistical analysis of the general death-rates of other cities 
to be assigned by instructor. 

4. Find the median death-rate for the counties of New York state 
for 1910. 

5. Compare the seasonal mortalities of San Francisco and Boston 
for 1910, using several different methods of statement. 



CHAPTER X 
STATISTICS OF PARTICULAR DISEASES 

In studying particular diseases we commonly use four 
ratios which, though described in different ways, may be 
distinguished by the terms, (a) mortality rate; (6) propor- 
tionate mortality; (c) morbidity rate and (d) fatality or 
case fatality. In addition to these ratios the number of 
cases of a particular disease may be arranged in groups and 
classes, by age, sex, nationality, occupation, date of onset 
and in other ways without using ratios; and the same is 
true of deaths from a particular disease. 

Mortality rate. — The mortality rate for a particular 
disease is obtained. by dividing the number of deaths from 
that disease by the mid-year population expressed in hundred 
thousands. 

Proportionate Mortality. — The proportionate mortality 
of a particular disease is the per cent which the number of 
deaths from that disease is of the total number of deaths 
from all causes. The interval of time is usually taken as 
one year, but shorter periods may be used. This method is 
sometimes spoken of as the percentage of mortality, or 
per cent distribution. 

Percentages of mortality are not as commonly published 
as they were some years ago. They do not involve the 
population, hence they are especially useful where the popu- 
lation is not known or cannot be correctly estimated. Since 
the custom of estimating population by a uniform system 
has become, general there has been less need for considering 

308 



INACCURACY OF MORBIDITY AND FATALITY RATES 309 

the percentage of mortality. A theoretical disadvantage of 
the method is the fact that the number of deaths from the 
particular disease appears in both the numerator and the 
denominator of the fraction; that is, the number of deaths 
from the particular disease helps to make up the total 
number of deaths. 

Morbidity rate. — The morbidity rate is the ratio between 
the number of cases of a particular disease in a year and the 
mid-year population expressed, in thousands, or better in 
hundred thousands. It is sometimes called the ''case rate." 
The morbidity rate is very useful in epidemiological investi- 
gations. It is usually based on the entire population, but just 
as in the case of death-rates, or mortality rates, from particular 
diseases it may be computed for specific age-groups or classes. 

Fatality. — The fatality of a disease is the ratio between 
the number of deaths and the number of cases. It is best 
expressed as a percentage. The fatality of any disease is 
far from being the same at all ages. 

Example. — In 1915 the population of Cambridge, Mass., 
was 108,822; the total number of deaths from all causes 
1460; the number of cases and deaths from scarlet fever 
were 379 and 5, respectively. From these facts we have the 
following rates and ratios: 

General death-rate, 1460 ^ 108.822 = 13.45 per 1000. 
Scarlet-fever, mortality rate, 5 -^ 1.08822 = 4.6 per 100,000. 
Scarlet-fever, proportionate mortality, 5 -^ 14.60 = 0.34 per cent. 
Scarlet-fever, morbidity rate, 379 ^ 1.08822 = 347 per 100,000. 
Scarlet-fever, fatality, 5 -r- 379 = 1.32 per cent. 

Inaccuracy of morbidity and fatality rates. — It must 
not be forgotten that rates for morbidity are based on re- 
ported cases and that not all cases are reported. Nearly all 
morbidity rates are too low. It follows therefore, that 
nearly all fatality percentages are too high. In the case of 
typhoid-fever, for example, a comparison of deaths and 



310 



STATISTICS OF PARTICULAR DISEASES 



reported cases, has led to the popular idea that the fatality is 
about 10 per cent, that is, one death for every ten cases. 
But in a number of epidemics, where the cases were accurately 
obtained by a house to house canvas, it has been found that 
there were from twelve to fifteen cases for each death, that 
is, the fatality was only about 7 per cent. 

It is interesting to see how an epidemic of typhoid fever 
will result in an increased proportion of cases being reported. 
In Cleveland, Ohio, in the year 1902 there were but 3.7 times 
as many reported cases as deaths, but the following year, 
when a severe epidemic occurred, there were 7.3 times as 
many reported cases as deaths. If the figures for 1902 had 
been correct it would have meant a fatality of 27 per cent, 
which is most unlikely. 

Causes of death in Massachusetts. — In 1915 the prin- 
cipal causes of death in Massachusetts were as follows. 
They are arranged according to the Abridged International 

List. 

TABLE 78 

PRINCIPAL CAUSES OF DEATH IN MASSACHUSETTS 



Rank. 



(1) 



1 

2 
3 
4 
5 
6 
7 
8 
9 

10 



Cause of death. 



(2) 



Pneumonia (92) 

Tuberculosis of the lungs (28, 29) 

Organic diseases of the heart (79) 

Diarrhea and enteritis (104) 

Congenital debility and malformations (150, 151). . 

Cerebral hemorrhage and softening (64, 65) 

Cancer and other malignant tumors (39-45) 

Acute nephritis and Bright's disease (119, i20) . . . . 
Other diseases of respiratory system (86-88, 91, 

93-98) 

Violent deaths, suicide excepted (164-186) 



Per cent of 
mortality. 



(3) 



8.8 
8.3 
7.4 
6.9 
6.8 
6.1 
5.e 
5.6 

4.8 
4.4 



It will be seen that these ten causes account for nearly two- 
thirds of all the deaths. 



STUDY OF TUBERCULOSIS BY AGE AND SEX 311 

The ten most important causes of death for the U. S. 
registration area in 1914 were not placed in the same order, 
but were as follows: 

TABLE 79 
PRINCIPAL CAUSES OF DEATH: UNITED STATES, 1915 



Rank. 


Cause of death. 


(1) 


(2) 


1 


Organic diseases of the heart (79) 


2 


Tuberculosis of the lungs (28, 29) 


3 


Bright's disease (119, 120) 


4 


Pneumonia (92) 


5 


Violent deaths (164r-186) 


6 


Cancer (39-45) 


7 


Cerebral hemorrhage (64, 65) 


8 


Congenital debility and malformations (150, 151) 


9 


Diarrhea and enteritis (104) 


10 


Bronchitis (89, 90) 



The proportionate mortality differs more or less in different 
places. It is not the same for the two sexes. It differs 
greatly at different ages. It is not the same at all seasons. 
It is different to-day from what it was a generation ago. The 
control of communicable diseases has considerably altered 
the relative importance of the different causes of death. 

Study of tuberculosis by age and sex. — In attempting to 
study any particular disease in order to determine its relation 
to age and sex one will be surprised to find how difficult it is 
to get a complete statement of the necessary facts for any 
given place. Obviously we need to have both the cases 
and deaths classified by age and sex, and we also need the 
population and the deaths from aU causes arranged by sex 
and according to the same age grouping. If we attempt to 
use the U. S. Census reports we find that no data for cases 
are given; if we attempt to use the state board of health 



312 STATISTICS OF PARTICULAR DISEASES 

reports we may find that the deaths are classified by age and 
sex, but that only the total numbers are given for cases; in 
some city board of health reports we may find cases and 
deaths duly classified but no populations given for the 
corresponding groups and classes. As an illustration of un- 
satisfactory current practice let us study the statistics of 
tuberculosis for the city of Cambridge, Mass., for the year 
1915. The data in the following table were taken from the 
annual report of the local board of health, except the popu- 
lation statistics, which were taken from the state census of 
that year. These data are more than ordinarily complete, 
yet they are not satisfactory, due chiefly to incomplete 
reports of cases. It may be assumed that the numbers of 
deaths are reasonably precise, yet they do not strictly 
represent local conditions as they include deaths in hospitals. 

The numbers of cases and deaths are small and this also 
makes the derived rates subject to erratic fluctuations. 

The fundamental data are given in columns (2) to (9), the 
derived figures in the subsequent columns. Column (10) 
was obtained from columns (2) and (8); column (12) from 
column (8) ; column (14) from columns (6) and (2) ; column 
(16) from column (6) ; column (18) from columns (6) and (4) ; 
column (20) from columns (6) and (8). 

If we take the figures at their face value we notice first 
that both the morbidity and mortality rates are high in 
infancy and low in childhood. The male morbidity rate 
reaches its highest point in age group 30-39 years, but the 
male mortality rate is highest between 40 and 50. In females 
the morbidity rate rises earlier and is highest in age-group 
20-29. The highest female mortality rate is also found in 
the same group. Forty per cent of all the cases and 37.9 per 
cent of all the deaths from tuberculosis among females oc- 
curred between the ages of twenty and thirty. 

If we study the figures for proportionate mortality we see 



STUDY OF TUBERCULOSIS BY AGE AND SEX 313 



TABLE 80 

CAMBRIDGE, MASS., 1915 

Statistics of Tuberculosis (28-35) Cases and Death, Arranged by 

Age and Sex 





Population. 


Deaths, all 
causes. 


Tuberculosis 
Deaths. 


Tuberculosis 
Cases. 














group. 


6 


03 


si 


ai 


6 


c3 


dj 


6 

03 




03 


s 


C3 


p 


a 


g 


03 


g 




S 


a 
fo 


^ 




§ 


r"^ 


S 


0) 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


0-1 


1,114 


1,080 


138 


105 







1 


1 


1-4 


4,161 


4,120 


38 


40 


2 




6 ' 


1 


5-9 


4,996 


5,000 


13 


13 







4 


5 


10-14 


4,488 


4,533 


7 


6 


1 




4 





15-19 


4,569 


4,901 


22 


12 


9 




. 9 


17 


20-29 


10,424 


11,326 


44 


51 


23 


31 


40 


50 


30-39 


8,334 


9,190 


64 


43 


29 


19 


49 


31 


40-49 


6,552 


7,177 


80 


78 


32 


10 


31 


9 


50-59 


4,133 


4,823 


88 


85 


13 


6 


14 


8 


60- 


3,224 


4,678 


229 


306 


10 


5 


9 


3 


Total 


51,995 


56,808 


723 


737 


119 


82 


167 


125 



Age- 


Morbidity 

(case), 
rate per 
100,000. 


Percentage 

distribution 

of cases. 


Mortality 

(death) 

rate. 


Percentage 
distribution 
of deaths. 


Proportion- 
ate mortal- 
ity, per cent. 


Fatality, 
per cent. 




'a 


6 

s 


6 


S 
fa 


6 


6 

c3 
S 

fa 


_6 


6 

ci 

B 

o 

fa 


6 


6 

03 

a 

fa 


_a5 


6 

a 

(B 

fa 


(1) 


(10) 


(11) 


(12) 


(13) 


(14) 


(15) 


(16) 


(17) 


(18) 


(19) 


(20) 




(21) 


0-1 


90 


93 


0.6 


0.8 





93 





1.2 





1 


100 


1-4 


144 


41 


3.6 


0.8 


48 


41 


1.7 


1.2 


5 


3 


33 


100 


5-9 


80 


100 


2.4 


4.0 





20 





1.2 





8 





20 


10-14 


89 





2.4 


0.0 


22 


26 


0.8 


1.2 


14 


17 


25 




15-19 


197 


347 


5.4 


13.6 


197 


143 


7.6 


8.5 


39 


58 


100 


41 


20-29 


383 


441 


23.8 


40.0 


220 


274 


19.3 


37.9 


52 


61 


57 


62 


30-39 


588 


337 


29.4 


24.8 


348 


207 


24.4 


23.2 


45 


44 


59 


61 


40-49 


473 


125 


18.6 


7.2 


488 


139 


26.9 


12.2 


40 


13 


103 


111 


50-59 


339 


166 


8.4 


6.4 


315 


124 


10.9 


7.3 


15 


7 


92 


75 


60- 


279 
321 


64 
220 


5.4 
100.0 


2.4 
100.0 


310 


107 


8.4 
100.0 


6.1 
100.0 


4 
16.5 


2 
11.1 


111 
71 


167 


Total 


229 


144 


66 



314 STATISTICS OF PARTICULAR DISEASES 

that tuberculosis caused 16.5 per cent of 'all deaths among 
males and 11.1 per cent of all deaths among females. In age- 
group 20-29 this disease caused nearly two-thirds of all 
deaths of females and more than half of all deaths of males. 
In comparing the figures for proportionate mortality it should 
be observed that the age-groups are not of equal value 
throughout the table; some cover ten years, some five, one 
covers four years, and one only one year. 

The fatality rates are practically worthless. Sometimes the 
number of reported cases was less than the number of deaths, 
thus making the fatality rate higher than 100 per cent. This 
would be an absurdity, if we did not know that the tuber- 
culosis deaths of one year may represent cases of the year 
before or the year before that. Tuberculosis is a disease of 
long duration, sometimes several years. The fatality of such 
a disease as this cannot be computed in this way. Yet 
imperfect as these figures are we can gather from them the 
main facts. We can see that tuberculosis is essentially a 
disease of early manhood and womanhood, and at those ages 
we naturally look to working conditions as contributory 
factors. The disease continues as an important cause of 
death up to old age, especially among males. 

If we take the figures for the U. S. Registration Area as* 
given in the Mortality Report for 1914 .we obtain a more 
uniform set of figures, as they are based on 898,059 deaths 
instead of 1460 deaths. (Table 81.) Here the highest 
proportionate mortality for tuberculosis was for age-group ^ 
20-24 years; for males it was 34.3 per cent, for females 39.2. . 
These figures are considerably lower than for Cambridge. 
The percentage distribution of tuberculosis deaths showed 
a maximum in age-group 20-24 for females, and in age-group 
25-29 for males. The morbidity, mortality and fatality 
could not be computed as no records of cases and no popula- 
tion by age-groups were given in the Mortality Report. 



DISTRIBUTION OF DEATHS FROM TUBERCULOSIS 315 

TABLE 81 

DEATHS FROM TUBERCULOSIS OF THE LUNGS (28) 
U. S. Registration Area, 1914, by Age and Sex 



Age- 


Deaths, all causes. 


Deaths (28) 


Percentage 
distribution. 


Proportionate 
mortality. 


group. 




















Male. 


Female. 


Male. 


Female. 


Male. 


Female. 


Male. 


Female. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


0-4 


118,375 


95,735 


3,416 


2,832 


6.1 


6.9 


2.9 


3.0 


5-9 


10,162 


9,140 


832 


878 


1.5 


2.1 


8.2 


9.6 


10-14 


6,819 


6,054 


702 


1,235 


1.3 


3.0 


10.3 


20.3 


15-19 


10,934 


10,322 


2,719 


3,801 


4.9 


9.2 


24.8 


36.8 


20-24 


17,516 


15,408 


6,002 


6,061 


10.8 


14.7 


34.3 


39.2 


25-29 


19,407 


16,300 


6,634 


5,795 


11.9 


14.1 


34.0 


35.5 


30-34 


20,212 


15,878 


6,466 


4,701 


11.6 


11.4, 


32.2 


29.7 


35-39 


23,154 


17,155 


6,428 


3,922 


11.5 


9.5 


27.8 


22.9 


40-44 


24,116 


16,803 


5.761 


2,950 


10.3 


7.2 


23.8 


17.6 


45-49 


25,283 


17,779 


4,640 


2,172 


8.3 


5.3 


18.3 


12.2 


50-54 


28,809 


20,294 


3,853 


1,679 


6.9 


4.1 


13.4 


8.3 


55-59 


28,896 


21,006 


2,905 


1,388 


5.2 


3.4 


10.1 


6.6 


60-64 


31,255 


24,275 


2,139 


1,217 


3.8 


3.0 


6.8 


5.0 


65-69 


32,728 


27,075 


1,460 


966 


2.6 


2.3 


4.5 


3.6 


70-74 


32.760 


29,109 


929 


777 


1.6 


1.9 


2.8 


2.7 


75-79 


27,365 


26,410 


515 


465 


0.9 


1.1 


1.9 


1.8 


80-84 


19,132 


20,537 


188 


205 


0.3 


0.5 


1.0 


1.0 


85-89 


9,600 


11,447 


48 


57 


0.1 


0.1 


0.5 


0.5 


90-94 


3,129 


4,165 


9 


16 






0.3 


0.4 


95-99 


704 


1,007 


6 


3 










100- 


179 


288 


1 


2 










Total 


491,416 


406,643 


55,724 


41,179 


100.0 


100.0 


11.4 


10.2 



Seasonal Distribution of deaths from tuberculosis. — A 

natural way of studying the seasonal distribution of deaths 
from tuberculosis is to subdivide the annual number of deaths 
into the numbers which occurred each month and then find 
what per cent each is of the whole. It is common to arrange 
the results in a horizontal line thus: 



316 



STATISTICS OF PARTICULAR DISEASES 



TABLE 82 

SEASONAL DISTRIBUTION OF DEATHS FROM TUBER- 
CULOSIS (28-35) 

U. S. Registration Area, 1914 







A 




• •-H 


>, 


oj 


ik 


bi 


+i 




> 


6 


"3 




03 


pin 


S 
S 




c3 


IS 






< 




O 


o 


0) 


-1^ 
o 


(1) 


(2) 


(3) 


(4) 


(5) 
8238 


(6) 

7782 


(7) 
6901 


(8) 
6528 


(9) 
6209 


(10) 
6031 


(11) 
6009 


(12) 


(13) 


(14) 


Number of deaths .... 


7522 


7524 


8537 


6212 


6873 


84,366 


Per cent of total for the 




























year 


8.9 


8.9 


10.5 


9.8 


9.2 


8.1 


7.6 


7.4 


7.1 


7.1 


7.4 


8.0 


100.0% 



These figures show that the largest numbers of deaths 
occur during the spring months, but the difference between 
winter and summer is not great. It must not be forgotten 
in such a comparison as this that the months are of unequal 
length. While the above figures show that 8.9 per cent of 
the deaths occurred in February and 10.5 per cent in March 
the average number of deaths per day was 269 per day in 
February and 275 per day in March. The U. S. Mortality 
Report, from which these figures were taken, do not dis- 
tribute the deaths in each month according to age. 

Another way of studying the seasonal distribution is to 

find the proportionate mortality for tuberculosis for each 

month. 

TABLE 83 

PROPORTIONATE MORTALITY FROM TUBERCULOSIS 
BY MONTHS (28-35) 

U. S. Registration Area, 1914 









n 


^ 

g 




1-5 


in 

< 




o 
O 

(10) 


> 

o 
"A 

(11) 


0) 

Q 
(12) 




(1) 


(2) 


(3) 

9.5 


(4) 


(5) 


(6) 

13.3 


(7) 


(8) 


(9) 


(13) 


9.1 


9.7 


10.1 


10.2 


9.3 


8.7 


8.8 


8.8 


9.0 


9.1 


9.4% 



Here the highest per cent was found in June. These figures 
are influenced, of course, by the numbers of deaths from 
causes other than tuberculosis. 



CHRONOLOGICAL STUDY OF TUBERCULOSIS 317 

ChronologicaK study of tuberculosis. — The death-rate 
from tuberculosis has decreased steadily during the last 
generation in Massachusetts as shown by Fig. 50. This 
curve does not tell us many of the things which we desire to 



ISO 
300 
^.50 

'SO 


D 




















V 


y 








Z5 


e3fh . 


{?^ff> 








\/ 


^ 






na 


fro 
(2SLln2/. 


)f/n/? 
















M'^ 




/^telts- 














V 




/67S-/ 


9/4- 














\ 




















V, 


\ 




















\ 
























\x 




















V 


\, 




'OO 


















^ 








^ 


















so 



































































/S70 mS /SeO /<9SS /SSO /S9S /SOO /SOS /^/O /S/S /920 

Yesrs 

Fig. 50. — Death-rates from Tuberculosis, Massachusetts, 1873-1914. 



know. It shows that prior to 1885 the death-rate exceeded 
300 per 100,000 but that now it is in the vicinity of 100. It 
is not decreasing arithmetically, however. Tuberculosis will 
not disappear by 1940, or thereabouts as one might think by 
a hasty forward projection of the plotted line. The curve is 



318 



STATISTICS OF PARTICULAR DISEASES 



losing slope. Even if the rate of decrease remained the same^ 
from year to year, it would take many, many years for the 
curve to reach the zero line. 

The curve does not tell us whether it is the lives of the 
young or the old which are being saved. It is not easy to 
obtain specific death-rates for tuberculosis by sex and age- 
groups which cover a long period of years. Even if we had 
the figures they would not be very reliable because of changes 
which are being made in the diagnosis of the disease. 

Tuberculosis and occupation. — Many misleading statis- 
tics relating to tuberculosis and occupation are continually 
being published. ■ As statements of facts they may be 
correct, but they are often subject to the fallacy of concealed 
classification and therefore give false impressions. 
' A recent report of the New Jersey State Department of 
Health gives statistics of deaths from tuberculosis in 1916 
classified by age and occupation. This is a better arrange- 
ment than is sometimes used, but even in studying these 
figures, it is necessary to be on guard against wrong con- 
clusions because of inadequate data. Thus we find the 

following: 

TABLE 84 

DEATHS FROM TUBERCULOSIS CLASSIFIED BY AGE AND 
OCCUPATION: NEW JERSEY, 1916 



Class. 


Age. 


Total 


10-19 


20-29 


30-39 


40-49 


50-59 


60-69 


70-79 


80-89 


90+ 


(1) 


(2) 


(3) 


(4) 


(5) 
1 

3 

31 

269 

96 

2 


(6) 


. (7) 


(8) 


(9) 


(10) 


(11) 


Farmers 


47 

11 

110 

858 

364 

19 


2 

2 

11 

34 

12 




6 

2 

45 

276 

61 




9 

1 

20 

158 

115 

4 


11 

2 
2 

65 
49 

7- 


9 
1 
1 

36 

27 
5 


6 



18 
4 

1 


3 



1 







Farm laborers 

Clerks 






Housekeepers and 
stewards 


1 


General laborers 

Stone cutters 







TUBERCULOSIS DEATH-RATE 319 

Why is the number of deaths from tuberculosis so high 
among housekeepers? Not because housekeeping imposes 
a special hazard, but because there are so many housekeepers 
in the state. Obviously what is needed here are the specific 
rates for this particular disease by age-groups. But to 
compute them it is necessary to know how many housekeepers 
there are in the state in each age-group, and who knows these 
facts? Also are the '' stewards " referred to male or female ? 

Why is the number of deaths among stone cutters so 
small? This occupation is certainly hazardous from the 
standpoint of tuberculosis, as the fine, sharp, stone dust 
tends to lacerate the lungs. We cannot draw any rehable 
conclusion from the figures because we do not know how 
many stone cutters there are in each group. 

We notice that the largest number of deaths from tuber- 
culosis among farmers occurred in age-group 50-59, but that 
among farm laborers in age-group 30-39. What is> farmer 
and what is a farm laborer? We must know that. Also do 
farm laborers ultimately become farmers? Is there a shift- 
ing of individuals from one class to the other as they grow 

older ? 

So also in the case of clerks. The largest number of 
deaths is in age-group 20-29. Do the clerks die off at this 
early age or do they cease to be clerks? Are the clerks male 

or female ? 

The student of statistics must persistently cultivate this 
critical faculty until it becomes a habit. It may>esult in a 
cynical and pessimistic frame of mind in regard to published 
vital statistics, but even this is better than an easy lapse into 
an unthinking acceptance of all statistics at their face value. 
Statistics should be used with truth or they had better not 

be used at all. 

Racial composition of population and tuberculosis death- 
rate. — The following interesting and at first puzzling 



320 



STATISTICS OF PARTICULAR DISEASES 



situation will serve to emphasize the importance of the 
careful analysis of death-rates and the necessity of taking 
into account not only specific death-rates but the composi- 
tion of the population. 

In 1910 the death-rate from tuberculosis of the lungs was 
226 per 100,000 in Richmond, Va., and 187 in New York 
City, and yet the specific death-rates from this disease for 
both white and colored persons were greater in New York 
than in Richmond. The following figures were taken from 
the U. S. Census reports. 



TABLE 85 

TUBERCULOSIS DEATH-RATES IN NEW YORK AND 

RICHMOND 



Class. 


Population. 


Number of deaths. 


Death-rate per 
100,000. 


New 
York. 


Rich- 
mond. 


New 
York. 


Rich- 
mond. 


New 
York. 


Rich- 
mond. 


(1) 


(2) 


(3). 


(4) 


(5) 


(6) 


(7) 


White 

Colored 

Total 


4,675,174 

91,709 

4,766,883 


80,895 

46,733 

127,628 


8368 
513 

8881 


131 
155 

286 


179 
560 

187 


162 
332 
226 



The explanation of this anomaly lies, of course, in the fact 
that in Richmond more than one-third of the population is 
colored, while in New York the colored population is less 
than two per cent. 

Many similar comparisons can be found between northern ' 
and southern cities. This is merely a striking case. 

Diphtheria in Cambridge, Mass. — Applying the same 
methods to the study of diphtheria we have the following 
figures: 



DIPHTHERIA IN CAMBRIDGE, MASS. 



321 



TABLE 86 

CAMBRIDGE, MASS., 1915 

Statistics of Diphtheria, Cases and Deaths Arranged by Age and Sex 









Deaths, all 


Death 


s from 


Cases of 


Age- 




causes. 


diphtheria. 


diphtheria. 


group. 




















Male. 


Female. 


Male. 


Female. 


Male. 


Female. 


Male. 


Female. 


...-, (1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


0-1 


1,114 


1,080 


138 


105 


1 


3 


7 


4 


1-4 


4,161 


4,120 


38 


40 


4 


6 


56 


67 


5-9 


4,996 


5,000 


13 


13 


5 


5 


63 


80 


10-14 


4,488 


4,533 


7 


6 


1 


1 


15 


24 


15^19 


4,569 


4,901 


22 


12 


1 





7 


4 


20-29 


10,424 


11,326 


44 


51 


1 





8 


12 


30-39 


8,334 


9,190 


64 


43 








4 


5 


40-49 


6,552 


7,177 


80 


76 











1 


50-59 


4,133 


4,823 


88 


85 











1 


60- 


3,224 


4,678 


229 


306 














Total 


51,995 


56,808 


723 


737 


13 


15 


160 


198 



Age- 


Morbidity 
(case) rate 
per 10,000. 


Percentage 

distribution 

of cases. 


Mortality 

(death) 

rate. 


Percentage 

distribution 

of deaths. 


Proportion- 
ate mortal- 
ity, per cent. 


r^atality, 
per cent. 


group. 


_a5 


a 

fa 




i 

fa 


6 

a 


j5 

S 

fa 




g 

fa 




S 

fa 


6 

"3 


a 

fa 


(1) 


(10) 


(11) 


(12) 


(13) 


(14) 


(15) 


(16) 


(17) 


(18) 


(19) 


(20) 


(21) 


0-1 


629 


371 


4.4 


2.0 


90 


278 


. 7.7 


20.0 


0.7 


« 

2.8 


14 


75 


1-4 


1340 


1630 


3 .0 


33.9 


96 


146 


30.7 


40.0 


10.5 


15.0 


7 


9 


5-9 


1262 


1600 


39.3 


40.4 


100 


100 


38.5 


33.3 


38.4 


38.4 


8 


6 


10-14 


334 


528 


9.4 


12.1 


22 


22 


7.7 


6.7 


14.3 


16.7 


7 


4 


15-19 


153 


82 


4.4 


2.0 


22 





7.7 


0.0 


4.5 


0.0 


14 





20-29 


76 


106 


5.0 


6.1 


9 





7.7 


0.0 


2.2 


0.0 


13 





30-39 


48 


55 


2.5 


2.5 








0.0 


0.0 


0.0 


0.0 








40-49 





14 


0.0 


0.5 








0.0 


0.0 


0.0 


0.0 








50-59 





21 


0.0 


0.5 








0.0 


0.0 


0.0 


0.0 








60- 








0.0 
100.0 


0.0 
100.0 








0.0 


0.0 


0.0 


0.0 
2.0 








Total 


308 


349 


25 


26 


100.0 


100.0 


1.8 


8 


7 



322 



STATISTICS OF PARTICULAR DISEASES 



Here we see that the maximum age incidence occurs be- 
tween the ages of one and ten for both males and females. 
The morbidity rate in Cambridge for this year was higher 
for females than for males, but the percentage distribution 
of the cases was about the same for the two sexes. The 
mortality rates followed the morbidity rates rather closely, 
and the fatality was fairly constant except for infant females. 
The proportionate mortality was highest in age-group 5-9. 
It must be remembered that these rates are computed from 
small numbers of cases and deaths, hence no very uniform 
or significant conclusions can be drawn from them. It is 
only by using large numbers of events that significant 
tendencies can be shown. The differences between the 
occurrence of diphtheria and tuberculosis are, however, very 
striking. 

The seasonal distribution of reported cases of diphtheria 
was as follows: 

TABLE 87 

SEASONAL DISTRIBUTION OF DIPHTHERIA CASES: 
CAMBRIDGE, MASS., 1915 









o 


1 

< 




6 


1—) 


< 




O 


> 

o 




o 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


(10) 


(11) 


(12) 


(13) 


(14) 


Number of cases .... 


24 


35 


37 


44 


31 


32 


21 


15 


20 


25 


38 


36 


358 



It will be noticed that the lowest numbers were reported 
during the summer vacation months. 

Knowing that the incidence of the disease was greatest 
during the school ages does this indicate that schools played 
an important part in spreading the infection? Do these 
statistics prove it? If not, what other statistics would be 
necessaify to prove it ? 



AGE SUSCEPTIBILITY TO DIPHTHERIA 



323 



Age susceptibility to diphtheria. — Dr. Charles V. Chapin 
the Superintendent of Health, of Providence, R. I., has been 
in the habit of computing what he calls the attack rate. This 
is a ratio between the number of cases and the number of 
persons exposed, that is, all the members of the family where 
the disease occurred, including the cases and those who were 
removed from home after the disease developed. The follow- 
ing figures, given in Dr. Chapin's report for the year 1915, 
are based on a study of 53,280 exposed persons during 1889- 
1915. 

TABLE 88 

DIPHTHERIA ATTACK RATE: PROVIDENCE, R. I., 1915 



Age-group. 


Attack rate 
(per cent). 


Age- group. 


Attack rate 
(per cent). 


(1) 


(2) 


(1) 


(2) 


0-1 yr. 

1+ 

2+ 

3+ 

4+ 

5+ 

6+ 

7+ 

8+ 

9+ 
10+ 
11+ 


16.70 
43.65 
54.55 
55.61 
55.91 
53.99 
53.82 
49.33 
44.31 
40.91 
36.42 
35.35 


12+ yr. 
13+ 

14+ 

15+ 

16+ 

17+ 

18+ 

19+ 

20+ 
Adults 
Total 


31.12 
26.08 
22.41 
18.92 
18.58 
17.85 
16.86 
17.33 
23.56 
6.83 
25.45 



These figures indicate that the chance of exposed persons 
acquiring the disease in recognizable form is highest at age 
four and decreases steadily as the age increases. At the 
most susceptible period more than half of those exposed 
came down with diphtheria. 

It was found that between the years 1889 and 1915 out of 
6822 families who lived in houses where the disease existed 
in other families, only 474 of these exposed families were 



324 



STATISTICS OF PARTICULAR DISEASES 



attacked. This is only 6.9 per cent. In most of these cases 
of attacked famihes there had been some sort of intercourse 
with the infected famihes, that is enough to transmit the 
disease by contact. 

Fatality of diphtheria. — Dr. Chapin has also kept a 
careful record of the fatality of diphtheria in Providence. 
In 1884 it was 30 per cent, and a few years later it rose to 
42 per cent. Between 1895 and 1896 it dropped from 20 
per cent to 14 per cent, since which date it has fallen until 
now it is only about 8 per cent, that is, there is only one death 
for each 12 cases. The fatality is not the same at all ages as 
the following table ^ shows : 



TABLE 89 
DIPHTHERIA CASE FATALITY AT DIFFERENT AGES 







1889-1914. 






1915. 




Age. 




























Cases. 


Deaths. 


Fatality. 


Cases. 


Deaths. 


Fatality. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


0-1 


280 


96 


34.28 


21 


2 


9.52 


1+ 


706 


247 


34.99 


43 


6 


13.95 


2-4 


3,322 


69r 


20.98 


181 


24 


13.26 


5-9 


4,541 


460 


10.13 


219 


15 


6.85 


10-14 


1,801 


83 


4.61 


9 


3 


3.79 


15-19 


616 


26 


4.22 


20 


1 


5.00 


20+ 


1.670 


40 


2.39 


62 


2 


3.23 


Total 


12,936 


1649 


12.74 


625 


53 


8.48 



The greatest decrease in the fatality of the disease has 
occurred among young children. 

To a large extent the decreased fatality has been due to 
the use of antitoxin, which decreased the number of deaths. 
To some extent it may have been due to better diagnosis by 

1 Ann. Report Providence Supt. of Health, 1915, p. 64. 



URBAN AND RURAL DISTRIBUTION OF DIPHTHERIA 325 

culture. If this practice increased the number of recognized 
cases it would decrease the fatality rates. 

Diphtheria is a short disease. Hence the fatahty can be 
computed far more accurately than in the case of tubercu- 
losis. 

Chronological study of diphtheria. — Fig. 51 ^ shows 
the decrease in the death-rate from diphtheria in Massa- 
chusetts since 1873. In 1876 the rate was very high, about 
195 per 100,000. It has decreased very greatly until now it 
is usually less than 20 per 100,000. Recurrences of diph- 
theria have occurred at intervals of five or six years. After 
the great epidemic of 1876 there was no important recurrence 
until 1889, but after that recurrences were noted in 1894 and 
1900. Since then, thanks no doubt to preventive medicine, 
the recurrences have been so slight as to be almost un- 
noticed. 

What is the reason for these recurrences, for this periodic 
development of diphtheria? In a general way, whooping 
cough, scarlet fever, measles, all children's diseases, have 
similar recurrences. It is commonly explained on the theory 
of susceptibility. It has already been seen that the rate of 
attack of exposed persons is very high among young children. 
It is known, too, that one attack usually makes the victim 
relatively immune against a second attack. After a period 
of relative quiescence during which the class of susceptible 
children has been annually recruited it is natural to expect 
that an epidemic may spread. This is apparently what 
happened until the methods of preventive medicine came 
to be generally used. It probably still happens, but to a 
less extent than formerly. 

Urban and rural distribution of diphtheria. — It is not 
easy to obtain complete statements of the facts to show the 
differences between the occurrence of diphtheria in cities and 
1 State Sanitation, Vol. I, p. 167. 



326 



STATISTICS OF PARTICULAR DISEASES 



90 




\ 


















80 




\ 


















70 






















fiO 












ne:^^f/ 


? Rrjfi 


3 






f^ 










D/p/7. 


/c 


r 


CroL/L 






w 










M 




7 


fs 






'90 




V 


. 






/e76 


WS/4- 








Oo 






1 
















//O 






1 
















'00 






1 






^ 










90 






\ 


h 














80 






\ 


J\ 












* 


70 






^ 


-^ \ 




. 










60 












\ 










^0 












\ 


\ 








40 


J 










1 / 


\ 








'90 












1/ 


V 








po 














\ 


^"-^ 






/O 


















v- 


<■ 


























/S7S /880 /SSS /890 /a9S /900 /90S /9/0 /9/S /92i 

Fig. 51. — Death-rates from Diphtheria, Massachusetts, 1873-1914. 



STATISTICAL STUDY OF TYPHOID FEVER 327 

rural districts. Occasionally partial statements are pub- 
lished. In the annual report of the Michigan State Board 
of Health for 1916-17 it is stated that for the period 1904-15 
the morbidity rate was 213 per 100,000 in urban districts and 
82 in rural districts; the mortality rates for 1908-1915 were 
16.2 and 12.2 per 100,000 respectively. The fatahty was 
10.9 per cent for cities and 15.7 for urban districts. No 
separations were made according to age and sex and it is 
difficult to find these facts. There is, however, quite a 
difference in the age distribution of diphtheria between the 
city and the country. In general the average age of diph- 
theria cases, as well as of persons dying from this disease, is 
lower in the city. The following facts were taken almost 
at random from the Mortality Statistics of 1914: 

TABLE 90 

PERCENTAGE AGE DISTRIBUTION OF DEATHS FROM 

DIPHTHERIA 



Age. 


Cities. 


Rural states. 


New York. 


Boston. 


Vermont. 


New 
Hampshire. 


Maine. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


0+ 

1+ 

2+ 

3+ 

4+ 

5-9 (per year) 
10-19 
20-29 
30-39 


10.7 
25.9 
16.5 
13.7 
9.7 
3.7 
0.26 
0.14 
0.05 


7.7 

21.4 

13.7 

14.9 

6.0 

5.3 

0.6 

0.12 

0.06 


0.0 

5.2 

18.4 

18.4 

13.1 

6.3 

0.52 

0.0 

0.0 


6.7 

17.8 

11.1 

8.9 

17.8 

4.0 

1.55 

0.0 

0.0 


9.3 
10.5 
16.3 
9.3 
7.0 
7.0 
0.7 
0.23 
0.23 



Statistical study of typhoid fever. — Typhoid fever has 
been given a great deal of attention from the statistical 
point of view. Hundreds of scientific papers describing 



328 STATISTICS OF PARTICULAR DISEASES 

local outbreaks of the disease, variations in the typhoid fever 
death-rate and so on have been published. For the most 
part these have been extensive and not intensive studies. 
It is rather surprising, when we view this enormous mass of 
statistics, how little we know about certain important points, 
such as the morbidity and fatality rates at different ages. 
Our interest has been engrossed by the more important 
matter of causation. There are many ways in which the 
disease may be communicated from one person to another 
and this question must be answered for each particular out- 
break or epidemic. The interest in statistical studies of 
typhoid fever has, therefore, centered around the subject of 
correlation, a phase of statistics which we shall consider in 
Chapter XIII . It will be useful to consider at this point 
some of the fundamental relations of this disease to human 
beings. Those who are interested in the epidemiology of 
the subject are referred to the author's book on Typhoid 
Fever. This book, it should be said, is to-day somewhat 
out of date, although its historical value remains. 

Age distribution of typhoid fever. — The largest number 
of deaths from typhoid fever is generally found in age-group 
20-29 years. Table 91 shows the percentage distribution of 
deaths by ages according to the U. S. Census ^ for 1900. 

In the case of epidemics caused by a widely scattered in- 
fection, as through the public water-supply, the age dis- 
tribution of the deaths usually approximates these figures. 
If, however, the outbreak occurs in a school-house or is 
caused by infected milk, which is used more freely by children 
than by adults, the larger numbers of deaths may occur in 
the lower ages ; in fact, this is a test often applied in the study 
of typhoid fever outbreaks. 

1 Vital Statistics, Vol. Ill, Part I, page cxlvi. 



AGE DISTRIBUTION OF TYPHOID FEVER 



329 



TABLE 91 

PERCENTAGE DISTRIBUTION OF DEATHS FROM 
TYPHOID FEVER; UNITED STATES: 1900 



Age-group. 


Per cent of deaths. 


Age-group. 


Per cent of deaths. 


(1) 


(2) 


(1) 


(2) 


0-4 


4.09 


50-54 


3.52 


5-9 


5.05 


55-59 


2.55 


10-14 


5.20 


60-64 


1.95 


15-19 . 


11.23 


65-69 


1.12 


20-24 


17.78 


70-74 


0.91 


25-29 


15.09 


75-79 


0.34 


30-34 


11.46 


80-84 


0.11 


35-39 


9.12 


85-89 


0.09 


40-44 


5.77 


Total 


100.00 


45-49 


4.62 







If we take the specific death-rates by sex and ages we 
)btain the following figures: 



TABLE 92 

SPECIFIC DEATH-RATES FOR TYPHOID FEVER 

United States: 1900 



Age-group. 


Rate per 100,000. 


Age-group. 


Rate pel 


100,000. 












Males. 


Females. 




Males. 


Females. 


(1) 


(2) 


(3) 


(1) 


(2) 


(3) 


0-4 


12 


16 


45^49 


34 


29 


5-9 


15 


21 


50-54 


30 


30 


10-14 


17 


31 


55-59 


30 


33 


15-19 


45 


53 


60-64 


29 


33 


20-24 


66 


57 


65-69 


22 


40 


25-29 


61 


48 


70-74 


27 


43 


30-34 


53 


43 


75-79 


20 


23 


35-39 


4S 


39 


80-84 


10 


26 


40-44 


34 


37 


8.5-89 


16 


35 



330 



STATISTICS OF PARTICULAR DISEASES 



It will be noticed that these differences are not as great 
as in the previous table. This is because there are fewer 
persons living at the ages above 50 and even if the specific 
rate remained high there would not be as many deaths. It 
is for this reason that both the age distribution of deaths 
and the specific death-rate are important tabulations. The 
specific rates just given represent practical conditions and 
take into account the important element of exposure. The 
difference between the death-rates of males and females at 
ages 25-29 must not be regarded as having a physiological 
basis, for at those ages males are more exposed to the dis- 
ease than females. 

Except at times of epidemics typhoid fever is not a well- 
reported disease. It is difficult therefore to obtain reliable 
specific morbidity rates by sex and ages. Such as have been 
computed, however, show an age distribution very similar to 
that of deaths, but with a tendency towards larger per- 
centages of cases in the earlier years. 

The fatality of the disease at different ages is not as well- 
established as it ought to be. Computations by the author, 
by Newsholme, by A. W. Freeman,^ seem to warrant the 
following approximate figures: 

TABLE 93 
APPROXIMATE CASE FATALITY IN TYPHOID FEVER 



Age. 


Per cent. 


Age. 


Per cent. 


(1) 


(2) 


(1) 


(2) 



10 
20 
30 


15 

8 
15 
18 


40 
50 
60 
All ages 


21 
25 

14 1 



1 Case Fatality in Typhoid Fever, Public Health Reports, Dec. 8, 
1916. 



i 



SEASONAL DISTRIBUTION OF TYPHOID FEVER 331 




X 

I- 

x>; 

o)ce 

lO 

OS 
Q._i 

1° 

cc 

UJ 

a. 



Fig. 52. — Diagram Showing the Relation between Atmospheric Tem- 
perature and Seasonal Distribution of Typhoid Fever. (After Sedg- 
wick and Winslow.) 



332 STATISTICS OP PARTICULAR DISEASES 

It is probable, therefore, that there is much unreported 
typhoid fever among children, some of it doubtless unrecog- 
nized. 

Seasonal distribution of typhoid fever. — The seasonal 
distribution of typhoid fever appears to be closely related to 
the manner in which the infection is communicated. Nor- 
mally there appears to be a fairly close relation between 
typhoid death-rates and atmospheric temperature, as shown 
in Fig. 52. Water-borne typhoid is most common during 
the colder months of the year. Examples of seasonal dis- 
tribution of typhoid fever are to be found in many epidemio- 
logical studies. 

Chronological reduction in typhoid fever. — The reduc- 
tion in the amount of typhoid fever in the United States 
during the last twenty-five years has been general and steady. 
From being one of our most dreaded diseases it seems likely 
to almost disappear. This has been due to many things. 
George A. Johnson,^ in an exhaustive compilation of statistics, 
gives the chief credit to the purification of public water 
supplies by filtration, his conclusions being summed up in 
Fig. 53. His main contention is doubtless correct, but the 
purification of water is only one of many factors in the prob- 
lem. The safeguards thrown around milk and other foods, 
the better understanding of the idea of contact, the con- 
stantly decreasing number of typhoid carriers since the Civil 
War and since the purification of water-supplies, the recent 
extensive use of vaccination methods, have contributed to 
the present low and falling death-rates. The' typhoid-fever 
death-rates in many cities using unfiltered water-supplies 
have fallen along with the others. This, however, is no argu- 
ment against the need of water purification. It does show 
the need of very careful analysis of the data. Extensive 
studies, like those of Johnson, have their value, but they are 
1 The Typhoid Toll, Jour. Am. Water Works Assoc, June, 1916. 



:hronological reduction in typhoid fever 333 



38 




--J- 


y 


\ 


















- 


i8 


3b < 


N 


/ 




^v 
















- 


S4 


34 










V 


\y 


^ 












- 


S? 


^2 


- 




' 




\ 


/• 


\ 


y 










- 


30 


30 


- 
























- 


'>8 


28 


- 














\> 


\ 
\ 








- 


'>R 


26 
24 


- 














1 


yN 


V -i 






- 


?4 


- 
















\ 


y 


\ 




- 


99 


22 


- 


GROWTH OF 

WATER FILTRATION 

AND 

DECREASE IN 

TYPHOID FEVER DEATH RATE 

IN THE 

REGISTRATION CITIES 

OF THE 

UNITED STATES 


> 


/ 


\\ 




- 


20 


20 


- 






\ 




- 


18 


18 


- 








>\ 


I y 


16 


lb 


- 












11 


14 


- 








/ 


\ 


12 


12 
10 


- 


















y 






- 


10 


- 
















y 


/ 






- 


8 


8 
6 
4 


- 
















-' 








- 


g 


- 










,^- 


.^ 




LEGEND 
_.__ FUtered Water 
PoDulation 


- 


1 


- 


















Tv 


phoid Fever 
)eath Rate 


- 






• I 


? 


2 



^^^ 
























■ 


J 



-H M CO 

O O O o 

Oi a Ci a 



a> 05 



Fig. 53. — Relation between Typhoid Fever and Water Filtration. 

After Johnson. 



334 STATISTICS OF PARTICULAR DISEASES 

not to be compared in importance with more fully analyzed 
and more critical statistical studies. 

Statistics of cancer. — Let us now take up a disease which 
is quite different from tuberculosis, diphtheria and typhoid 
fever, namely, cancer. This involves some interesting appli- 
cations of statistical principles. The subject is one which 
demands most careful investigation and the reader should 
by all means read a paper on ''The Alleged Increase of 
Cancer," by Prof. Walter F. Willcox, of Cornell University, 
as a splendid example of critical work.^ 

Extensive studies of death-rates have shown that as a 
reported cause of death cancer is on the increase. Dr. F. L. 
Hoifman in a most elaborate monograph entitled ''The 
Mortality of Cancer throughout the World," ^ has demon- 
strated this fact. But is this reported increase an actual 
increase ? Is it due to changing conceptions of the statistical 
unit, to a better recognition of the disease, to differences in 
the composition of populations? Messrs. King and News- 
holme,^ take the ground that the alleged increase is due to 
statistical fallacies. Their conclusion is based on intensive 
studies. Willcox, in the article referred to, has made a critical 
comparison of these two points of view, and his conclusions 
are that "improvements in diagnosis and changes in age 
composition explain away more than half and perhaps all of 
apparent increase in cancer mortality." 

It is admitted at the start that no reliable statistics of 
cancer morbidity exist. Therefore, neither morbidity nor» 
fatality rates can be computed. The entire discussion rests 
on deaths. 

The increase in reported deaths from cancer is well shown 
by the following figures: 

1 Quar. Pub. Am. Sta. Asso., Sept. 1917, Vol. XV, p. 701. 

2 Published in 1915, by the Prudential Press, Newark, N. J. 

3 proc. Royal Society, 1893, liv, pp. 209-242. 



STATISTICS OF CANCER 



335 



TABLE 94 

DEATH-RATES FROM CANCER 

U. S. Registration Area of 1900 



Vpnr 


Rate per 100,000. 




Male. 


Female. 


(1) 


(2) 


(3) 


1900 
1905 
1910 
1915 


47.0 
53.0 
62.6 
72.3 


80.7 

92.1 

103.7 

111.9 



The death-rate for females is considerably higher than for 
males. 

The specific death-rate by ages and sex runs as follows: 

TABLE 95 

SPECIFIC DEATH-RATES FOR CANCER 

U. S. Registration Area of 1900 for the Year 1910 



Age-group. 


Rate per 100,000. 


Age-group. 


Rate per 100,000. 


Male. 


Female. 


Male. 


Female. 


(1) 


(2) 


(3) 


(1) 


(2) 


(3) 


0-5 

&-9 
10-14 
15-19 
20-24 
25-34 


4.1 
1.5 

1.8 
2.9 
4.9 
9.5 


2.8 
1.2 
1.4 
3.5 
4.1 
21.9 


35-44 
45-54 
55-64 
65-74 
75- 


33.0 
106.7 
272.0 
493.6 
693.7 


88.9 
230.7 
411.3 
616.2 

867.8 



By applying the method of adjustment to the Standard 
Million of Population, Willcox finds that for England and 
Wales in 1911 the death-rate from cancer should have been 



336 STATISTICS OF PARTICULAR DISEASES 

91.5 instead of 99.3 per 100,000. In 1901 it was 84.3; hence 
the increase would have been 8.7 per cent, instead of 17.8 
per cent, if computed on the basis of similar populations. 
Similar comparisons are made for other populations, from all 
of which the conclusion is drawn that about one-third of the 
increase in all the populations considered is due to changes 
in sex and age composition. 

In regard to diagnosis many interesting facts are presented. 
There are differences between the statistics for accessible and 
inaccessible cancer, the increase being chiefly in the latter. 
"Laymen seldom report cancer as a cause of death," and 
there appears to be a correlation between cancer increase 
and an increase in the number of physicians per 100,000 of 
population, and the number of medical certificates signed by 
competent persons. The increase in hospitals is also a 
factor. Deaths ascribed to tumor, and to "old age," have 
been decreasing, as cancer has increased, and the implication 
is that there has been a shifting of these statistical units. 
For all of these deaths the reader should consult Willcox's 
paper. He gives also, by way of analogy, a comparison 
between cancer and appendicitis, which shows that the rate 
of increase in reported causes of death are substantially the 
same for the two diseases, namely, 44 per cent and 40 per 
cent respectively between 1900 and 1915. The upshot of 
this investigation is that there is no more reason for people 
to fear dying from cancer now than there was a generation 
ago. The disease has not changed, people have not changedj 
it is the reports of the physicians which have changed because 
of their increased knowledge. Is this the last word on the 
subject? Probably not. 

Further studies of particular diseases. — It is not possible 
to take up the hundred or more particular diseases and 
discuss them by means of statistics. This, however, is one 
of the chief uses of vital statistics. Enough has been given 



EXERCISES AND QUESTIONS 337 

perhaps to illustrate the method of procedure, and to em- 
phasize the hiiportance of critical statistical analysis. The 
necessity of considering specific rates, and varying composi- 
tions of populations in all these studies cannot be too strongly 
insisted on. 

The student will find it a fascinating and highly valuable 
study to take up some disease in which he may be interested 
and study it intensively. There is room in statistical litera- 
ture for many monographs treating of the statistics of 
particular diseases. 



EXERCISES AND QUESTIONS 

1. Describe the cycles of whooping cough in New York State since 
1885. [N. Y. State Dept. of Health, Monthly Bulletin, March 1917 
p. 70.] 

2. How would you find out what proportion of all children born have 
whooping cough at some time in their lives? Try to ma.ke up a table 
from morbidity statistics of whooping cough classified by age in years, 
and see if you cannot determine this. Select, for example, the year 
1910. How many babies were born that year and how many had had 
whooping cough while infants? Tn 1911 how many cases of whooping 
cough were in age-group 1-2; in 1912 how many in age-groups 2-3, etc.? 
Add these together and compare the result with the births in 1910. 
Then do the same starting with 1909, and then 1908, etc. Compare all 
the results. Are they more uniform than the ordinary annual statistics 
for whooping cough? 

3. Make the same sort of study for measles. 

4. Make the same sort of study for diphtheria. 

5. Make the same sort of study for scarlet fever. 

6. Compare death-rates for whooping cough, measles, etc., in urban 
and rural districts. What foundation is there for Farr's law that 
contagious diseases increase as the density of population? 

7. Explain the recent finding that the death-rates from measles in 
the U. S. army cantonments has varied inversely as the density of 
population (percentage of urban population) in the states from which 
the soldiers came. 



338 STATISTICS OF PARTICULAR DISEASES 

8. Describe the periodicity of whooping cough in Sweden. (See 
Stephenson and Murray's Textbook of Hygiene.) 

9. Describe the age distribution of Pellagra. [See Amer. J. P. H., 
July, 1918, p. 488.] 

10. What reduction in diphtheria has occurred as a result of the use 
of anti-toxin. [See Am. J. P. H., May, 1917, p. 445.] 

11. Is appendicitis increasing? [See Am. J. P. H., July, 1916.] 

12. Make a statistical summary of the influenza epidemic of 1889-90. 
Consult reports of state and city departments of health. 

13. Make a statistical study of the influenza epidemic of 1918 for 
some state, city or town. 

14. Prepare a short statistical summary of cancer, — its geographi- 
cal distribution, its occurrence among different age-groups, its chro- 
nology, etc. [Hoffman, Frederick L. The Mortality from Cancer 
throughout the World. Newark. The Prudential Press, 1915.] 



CHAPTER XI 
STUDIES OF DEATHS BY AGE PERIODS 

Infant mortality. — No part of vital statistics is attracting 
more attention nowadays than the subject of infant mor- 
taUty. It is, indeed, a serious problem and worthy of most 
careful study. It is a complex problem and one difficult to 
understand. It is a problem which goes beyond itself. 
Newsholme says that '' infant mortahty is the most sensitive 
index of social welfare and of sanitary improvements which 
we possess." Another says that ''infant mortality is to the 
health officer what the clinical thermometer is to the physi- 
cian." People who will not take care of their offspring will 
not take care of themselves. 

Some definitions. — The term infant is applied to any 
child from the day of its birth up to one year of age. A child 
born dead is not regarded as having been born. It is not 
included among either births or deaths; it is a still-birth. 
But if the child is born alive and dies almost immediately it is 
to be regarded as an infant and both its birth and its death 
is to be recognized statistically. In the past health officials 
were not careful to make this distinction and many of the 
old statistics are for that reason not comparable with present- 
day records. This should be kept in mind in comparing 
statistics which extend over long periods of time. 

The specific death-rate for infants, that is, for age-group 
3-1, is computed in the same way as the specific death-rate 
For any other age-group, namely, by dividing the annual 
lumber of deaths in the group by the mid-year population of 

339 



340 



STUDIES OF DEATHS BY AGE PERIODS 



the group, expressed in thousands. By infant mortality, as 
the term is generally understood, is meant something shghtly 
different, namely, the number of infant deaths in a calendar 
year divided by the number of births during the same year. 
Prenatal deaths. — Foetal deaths which occur before the 
sixth or seventh month of gestation are known as miscarriages 
and are not reportable or recognized in ordinary statistical 
work; those which occur later than this are called still- 
births and must be reported. The time hmit is sometimes 
stated as twenty-eight weeks, sometimes it is made dependent 
upon the apparent condition of the foetus. Still-births, 
although reportable, should always be kept apart from true 

births. 

The following figures show how in Boston the ratio of still- 
births to total population and the ratio between still-births 
and living births have changed during the last twenty years. 



TABLE 96 
STILL-BIRTHS, BOSTON 





Number per 


Number per 




Number per 


Number per 


Year. 


100 living 


1000 inhabi- 


Year. 


. 100 hving 


1000 inhabi- 




births. 


tants. 




births. 


tants. 


(1) 


(2) 


(3) 


(1) 


(2) 


(3) 


1891 


4.2 


1.3 


1904 


4.0 


1.1 


1892 


4.2 


1.2 


1905 


4.2 


1.1 


1893 


4.1 


1.3 


1906 


3.8 


1.1 


1894 


4.5 


1.4 


1907 


4.0 


1.2 


1895 


3.8 


1.2 


1908 


3.4 


1.0 


1896 


3.9 


1.3 


1909 


4.0 


1.1 


1897 


3.6 


1.2 


1910 


3.0 


1.0 


1898 


3.7 


1.1 


1911 






1899 


3.3 


1.0 


1912 






1900 


3.5 


1.0 


1913 






1901 


3.6 


1.0 


1914 






1902 


3.9 


1.1 


1915 






1903 


4.0 


1.1 









INFANT MORTALITY 341 

The monthly records show no appreciable variation in the 
rate of still-births during the year. The ratio of still-births 
to living births is much greater for illegitimate than for legiti- 
mate children, especially, among mothers less than twenty 
years of age. There are marked differences in the still-birth 
rates in different countries. 

At Johnstown, Pa., 4.5 per cent of all births were still- 
births, and 8.7 per cent of all mothers reporting had suffered 
miscarriages. 

The percentages of still-births arranged according to the 
age of the mothers gave the very high percentage of 11.1 
per cent for mothers under 20 years of age, 4 per cent for age 
group 20-24, 5.1 for 25-29 years, 4.4 for 30-39 years, and 3.3 
for ages over 40. The percentage for native mothers was 
5.2 per cent, for foreign mothers, 3.8 per cent. 

Infant mortality and the specific death-rate for infants. — • 
There are two reasons why the specific death-rate for age 
group 0-1 year is not used more. The first is the difficulty 
of finding the actual number of infants alive at the middle of 
any calendar year. Of course, a census might be taken on 
July 1, but even that figure would not be very satisfactory 
for births are not uniformly distributed through the year 
and the ages of infants are often given incorrectly. It is 
possible to compute the number alive July 1 from the 
monthly records of births and deaths, but rarely, if ever, in 
this country are the data for doing this published. The 
reports of vital statistics of Hamburg contain each year a 
table like that shown in Table 97 from which this computa- 
tion can be made. 

Starting in 1911 we see that in January 1853 children were 
born, of which 260 died the same year; 5, however, died in 
January, 1912, before reaching their first birthday. Of the 
children born in February, 1911, 8 died in January, 1912, 
and 3 in February, 1912. By keeping up this tabulation we 



342 



STUDIES OF DEATHS BY AGE PERIODS 



TABLE 97 

BIRTHS AND DEATHS OF CHILDREN UNDER ONE YEAR 

Hamburg, 1911 and 1912 



Year 
and 


Births. 


Died 
in 
1911. 


Died in 1912 before reaching age of 
one year. 


Total 


Died 
in 

first 
year. 


Reached 

the first 

year alive. 


Liv- 
ing 


mo. 


J. 


F. 


M. 


A. 


M. 


J. 


J. 


A. 


S. 


0. 


N. 


D. 


No. 


% 


1913. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


(10) 


(11) 


(12) 


(13) 


(14) 


(15) 


(16) 


(17) 


(18; 


( ) 


(20) 


1911. 
Jan. 
Feb. 
Mar. 
April 
May 
June 
July 
Aug. 
Sept 
Oct. 
Nov. 
Dec. 


1,853 
1,700 
1,752 
1,713 
1,777 
1,670 
1,791 
1,760 
1,670 
1,668 
1,603 
1,705 


260 
254 
253 
250 
251 
242 
255 
188 
124 
131 
90 
58 


5 

8 

4 

6 

11 

11 

14 

15 

18 

19 

27 

5a 
























5 
11 
16 
25 
31 
45 
62 
70 
73 
99 
133 
179 


265 
265 
269 
275 
282 
287 
317 
258 
197 
230 
323 
237 


1,588 
1,435 
1,483 
1,438 
1,495 
1,383 
1,474 
1,502 
1,473 
1,438 
1,380 
1,468 


85.70 
84.41 
84.65 
83.95 
84.13 
82.81 
82.30 
85.34 
88.20 
86.21 
86.09 
86.10 




3 
6 
4 
3 

8 

8 

10 

11 

18 

27 
27 
























6 
12 
10 
11 

9 
12 

8 
17 

8 
25 

118 

30 
44 
63 




















3 

43 
7 

10 
6 
8 
6 

16 
14 

74 

19 
20 
29 
57 


































8 

4 

9 

11 

14 

8 

10 



13 

8 

6 

5 

15 

7 














4 
6 
2 
8 
9 
13 












4 

7 
4 
8 
9 










2 
6 
7 
3 








2 

5 

10 


3 
6 


2 


Sum 


20,662 


2356 


191 

78 


125 

45 
56 


67 

17 
12 
21 
37 
76 


54 

13 
15 
20 
17 
26 
60 


42 

12 
15 
15 
20 
20 
41 
68 


32 


18 


17 


9 


2 


749 


3105 


17,557 


84.97 


1912. 

Jan. 

Feb. 

Mar. 

April 

May 

June 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 


1,829 
1,722 
1,810 
1,721 
1,723 
1,777 
1,833 
1,817 
1,748 
1,781 
1,688 
1,799 




9 
15 
19 
19 
28 
26 
43 
70 


8 

9 

7 

6 

12 

21 

21 

25 

67 


4 
4 
6 
7 

12 
19 
19 
30 
27 
71 


9 

6 
15 

6 
13 

7 

16 
20 
25 
38 
69 


3 

3 

6 

8 

8 

12 

11 

21 

22 

33 

35 

70 


247 
199 
201 
177 
195 
186 
178 
166 
141 
142 
104 
70 








^,!)f^ 








1,51^ 








l.fif 














^,M 








1,52 


















1,5s 




















1,6£ 






















Ifil 
























\,U 


























Ific 




























1,5^ 






























1.7i 


Sum 


21,248 




78 


101 


137 


125 


163 


151 


191 


229 


176 


199 


224 


232 


2006 








19,2^ 










Died in year 1912.. 


269 


226 


255 


199 


230 


205 


233 


261 


194 


216 


233 


234 


2755 











FIRST-YEAR DEATH-RATE 343 

obtain all the deaths in 1912 of babies born in 1911. In the 
same way we obtain the deaths in 1912 of infants born in 
1912. These added to the preceding give us all the infant 
deaths for 1912, namely, 2755. The number of children 
living Jan. 1, 1913, was 21,248 - 2006, or 19,242. By 
starting with July 1, 1910, we could obtain the number of 
children living July 1, 1912. It requires monthly records 
extending over two years to get this result, and even after 
we get it it may not be exact as there may have been errors 
in the records. 

The infant mortality is much simpler to compute, but it is 
not without its errors. Birth reporting is notoriously bad, 
and there is often doubt as to the stated age of the dying 
child. Children within a few months of their first birthday 
are sometimes said to be a year old. 

In the long run, the average specific death-rates for age 
group 0-1 agree fairly well with the infant mortalities, but 
in any particular place and year they may vary from each 
other as much as twenty-five or fifty per cent. The infant 
mortality should be stated in whole numbers as the accuracy 
of the data does not warrant the use of decimals. 

The deaths of infants in one year will include some who 
were born in the preceding year. In our infant mortality 
ratios, therefore, we are not dealing wholly with the same 
infants in the denominator and numerator. Fluctuations 
in the birth-rate in successive years may influence this 
ratio. 

First-year death-rate. — In the case of Hamburg we see 
from the table that in the year 1912 there were 21,248 births 
and 2755 infant deaths. From these figures we may compute 
the infant mortality ratio in the usual way and obtain 130 
per 1000. Yet if we consider the 20,662 births in the twelve 
months of 1911 and follow them through their first year, we 
find that 3105 died, that is the ratio was 150 per 1000. In 



344 



STUDIES OF DEATHS BY AGE PERIODS 



other words, 850 per 1000, or 85 per cent reached, their first 
year of Hfe. 

In the printed table we find in the last column for 1911 
figures which show " these percentages by months. It is 
interesting to notice how this percentage of born children 
who reach their first year varies with the season. According 
to the 1911 figures for Hamburg, September is the most 
favorable month for a birth because 88.2 per cent of the 
children born that month reached the age of one year; 118 
per thousand died. July is the most unfavorable month as 
only 82.3 per cent reached the first year; 177 per thousand 
died. 

Very few American cities keep their records in such shape 
that facts like these can be easily secured. In Hamburg they 
publish both the infant mortality rates and the percentage 
of infants who die in their first year of life. They also pub- 
lish the proportionate infant mortality, that is, the per cents 
which the infant deaths are of the total deaths. It is in- 
teresting to compare these figures. 



TABLE 98 
INFANT DEATHS, HAMBURG 



Year. 


Proportionate 
mortality. 


Infant mortality (per 
1000 births.) 


Number of infants per 

1000 who died in th^ir 

first year. 


(1) 


(2) 


(3) 


(4) 


1908 
1909 
1910 
1911 
1912 


26.2 
23.7 
24.4 
23.4 
20.8 


156 
142 
149 
158 
130 


184 
159 
160 
159 
141 



This method of studying infant mortality by determining 
the percentage of first-year deaths was used in the Johns- 
town, Pa., investigation in 1914. It was here referred to as 



REDUCTION IN INFANT MORTALITY 345 

the ''absolute infant mortality," the conventional method 
of comparing births and infant deaths for a calendar year 
being regarded, as indeed it is, as an approximate method, 
chosen for convenience only. In Johnstown the results were 
obtained by an intensive study of individual infants. Con- 
trary to the results in Hamburg the ''percentage of first-year 
deaths" was less than the "infant mortality," the figures 
being 13.4 per cent (134 per 1000) and 165 respectively. 

Various methods of stating infant mortality. — It will be 
seen that infant mortahty may be expressed in various 
ways: 

1. Rate of deaths in first year— the true, or "absolute," 

method. 

2. Infant mortality, the calendar ratio between infant 

deaths and births — the common method. 

3. Specific death-rate for age-group 0-1 year — difficult 

to compute, but useful as hereafter shown. 

4. Proportionate mortality — the ratio between infant 

deaths and total deaths. 

5. Infant death-rate per 1000 inhabitants — a ratio rarely 

used and of little value. 

It should be noticed that all of these ratios except the first 
are calendar ratios, that is, they are based on one year or 
some other interval of time. The true rate of infant deaths 
considers the calendar only as to births, the period covered 
by the deaths being one year from the date of each birth. 
In the following paragraphs all of these ratios are used in 
order that the student may learn to discriminate between 
them. 

Chronological reduction in infant mortality. — The infant 
mortality rates in nearly all civilized countries are falling. 
In recent years the fall has been more rapid than it was a 
generation ago. In Sweden we have a very long record, a 
part of which is given in Table 99. Prior to 1800 the infant 



346 



STUDIES OF DEATHS BY AGE PERIODS 



TABLE 99 

INFANT AND CHILD MORTALITY IN SWEDEN 

1751 to 1900 by 5-Year Periods 



Period. 


Total death- 
rate per 1000. 


Age-group in years. 


0-1.1 


1-3.2 


3-5.2 


0-5.2 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


1751-55 


26.52 


205.75 


52.17 


27.31 


86.07 


1756-60 


28.25 


203.41 


49.50 


26.26 


81.64 


1761-65 


29.08 


221.73 


53.94 


28.49 


90.46 


1766-70 


26.38 


210.41 


50.12 


27.06 


85.14 


1771-75 


33.07 


212.89 


66.55 


36.15 


92.88 


1776-80 


24.86 


192.02 


56.21 


29.13 


83.74 


1781-85 


27.80 


193.98 


62.64 


36.16 


86.44 


1786-90 


27.61 


205.70 


48.78 


23.04 


81.67 


1791-95 


25.21 


192.59 


44.63 


20.76 


77.09 


1796-00 


25.65 


199.53 


48.02 


23.47 


79.55 


1801-05 


24.35 


186.08 


41.48 


18.70 


70.65 


1806-10 


31.45 


211.46 


59.09 


29.09 


87.42 


1811-15 


27.11 


191.76 


56.46 


20.57 


81.54 


1816-20 


24.63 


175.51 


45.93 


17.96 


71.00 


1821-25 


22.07 


158.85 


36.24 


14.33 


61.63 


1826-30 


25.10 


175.76 


37.72 


17.07 


64.53 


1831-35 


23.05 


167.31 


33.44 


14.44 


60.32 


1836-40 


22.53 


166.35 


35.47 


15.42 


60.31 


1841-45 


20.20 


153.77 


30.38 


14.39 


56.18 


1846-50 


20.95 


152.56 


33.39 


16.48 


57.34 


1851-55 


21.65 


148.89 


35.32 


18.79 


58.83 


1856-60 


21.73 


143.47 


39.12 


23.87 


61.96 


1861-65 


19.76 


136.17 


40.95 


21.78 


58.48 


1866^70 


20.54 


141.93 


38.78 


19.59 


56.14 


1871-75 


18.28 


133.57 


29.78 


14.64 


51.47 


1876-80 


18.26 


126.28 


36.26 


19.80 


53.01 


1881-85 


17.53 


116.08 


31.82 


17.09 


47.18 


1886-90 


16.37 


105.00 


25.88 


13.41 


40.06 


1891-95 


16.61 


102.76 


23.97 


12.65 


38.21 


1896-00 


16.12 


100.50 


21.78 


9.72 


35.65 



1 Per 1000 births during the given period, i.e., " infant mortality." 

2 Per 1000 of population at middle of period, i.e., specific death-rateSo 



HEDUCTION IN INFANT MORTALITY 



347 



mortality was upwards of 200, but by 1900 it was only about 
half as much. In Stockholm in 1912 it was only 82. 

In Massachusetts ^ the rate of infant mortality has varied 
as follows: 

TABLE 100 

RATE OF DEATHS DURING FIRST YEAR 

Massachusetts 



Year. 


Per 

1000. 


Year. 


Per 

1000. 


Year. 


Per 

1000. 


Year. 


Per 

1000. 


Year. 


Per 

1000. 


(1) 


(2) 


(1) 


(2) 


(1) 


(2) 


(1) 


(2) 


(1) 


(2) 


1851 


133 


1864 


154 


1877 


152 


1890 


167 


1903 


138 


1852 


126 


1865 


147 


1878 


150 


1891 


162 


1904 


133 


1853 


135 


1866 


138 


1879 


145 


1892 


162 


1905 


140 


1854 


131 


1867 


136 


1880 


163 


1893 


164 


1906 


138 


1855 


135 


1868 


140 


1881 


163 


1894 


163 


1907 


133 


1856 


123 


1869 


149 


1882 


163 


1895 


156 


1908 


134 


1857 


118 


1870 


162 


1883 


159 


1896 


158 


1909 


127 


1858 


122 


1871 


151 


1884 


159 


1897 


147 


1910 


133 


1859 


130 


1872 


194 


1885 


157 


1898 


151 


1911 


119 


1860 


134 


1873 


178 


1886 


155 


1899 


150 


1912 


117 


1861 


146 


1874 


164 


1887 


160 


1900 


157 


1913 


110 


1862 


131 


1875 


175 


1888 


162 


1901 


138 


1914 


106 


1863 


150 


1876 


158 


1889 


160 


1902 


140 


1915 


102 



The report speaks of these as ^'first-year deaths" but 
does not state how they were computed. Apparently the 
figures refer to infant mortality computed in the conventional 
way. The figures show a substantial decrease only during 
the last ten years. 

The following figures show the decrease in infant mortality 
computed in the conventional way between 1908 and 1915 
for Massachusetts, Boston and the remainder of the state 
outside of Boston. 

1 Mass. Registration Report, 1915, p. 153. 



348 



STUDIES OF DEATHS BY AGE PERIODS 



TABLE 101 
INFANT MORTALITY: MASSACHUSETTS 



Year. 


Massachusetts. 


Boston. 


Remainder of state. 


(1) 


(2) 


(3) 


(4) 


1908 


134 


149 


129 


1909 


127 


121 


129 


1910 


133 


127 


134 


1911 


119 


126 


118 


1912 


117 


117 


116 


1913 


110 


110 


110 


1914 


106 


105 


107 


1915 


102 


104 


101 



It would be possible to print page after page of such figures 
as these taken from the records of our American cities. 

In Boston the rate of infant deaths per 1000 of total 
population has decreased as follows: 



TABLE 102 
INFANT MORTALITY: BOSTON 



Year. 


Rate per 1000 of 
population. 


Year. 


Rate per 1000 of 
population. 


(1) 


(2) 


(1) 


(2) 


1875 
1880 
1885 
1890 


6.6. 
5.6 
5.5 
5.1 


1895 
1900 
1905 
1910 


5.1 
4.3 
3.7 
3.3 



This ratio is one which depends upon the number of 
children born as well as upon their rate of death, and involves 
the varying composition of the population as to age, mar- 
riage, nationality, and so on. ' 

Reasons for the decreasing infant mortality. — As most 
of the current discussions of infant deaths are based on the 



INFANT MORTALITY IN DIFFERENT PLACES 349 

calendar ratio between reported deaths of infants and reported 
births, it is well to remember that a falling ratio may result 
from an increase in the denominator as well as from a decrease 
in the numerator of the fraction. We have already learned 
that the birth registration is increasing in accuracy, that a 
larger percentage of births are reported now than formerly. 
This fact alone will account for a part of the drop in infant 
mortality; in some places it may account for nearly all of it. 
In comparing the infant mortality rates in different places 
this difference in the relative accuracy of reports of births 
and deaths must not be overlooked. To understand just 
what is being accomplished by present-day activities in 
infant welfare it is necessary to dig deeper into the subject 
and to analyze the statistics of infant births and deaths. 

Infant mortality in different places. — If we examine the 
statistics for different countries we shall discover greats 
differences in infant mortality. We have space here for only 
a few figures. 



350 



STUDIES OF DEATHS BY AGE PERIODS 



TABLE 103 
INFANT MORTALITY IN A FEW FOREIGN CITIES 



Cities. 


1881- 
1885. 


1886- 
1890. 


1891- 
1895. 


1896- 
1900. 


1901- 
1905. 


1906- 
1910. 


1911. 


1912. 


m (1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


London 


150 

127 

176 

173 
171 


153 

136 

175 

155 
173 

246 

152 

199 
207 

182 
168 

243 
320 

264 
260 

196 
200 

237 

238 

161 
209 


156 

140 

169 

138 
136 

237 
200 

135 

168 
191 

170 
158 

242 
316 

242 
226 

219 
194 

199 
233 

158 

151 


162 

144 

175 

130 
129 

258 
231 

119 

146 
167 

169 
152 

251 

286 

218 
182 

195 
170 

174 

218 

147 
120 


139 
131 

158 

107 
113 

271 
205 

110 

122 
144 

136 
119 

246 
262 

202 
174 

178 
163 

149 
201 

146 

93 


114 

119 

146 

85 
94 

261 
166 

106 

90 
105 

103 
96 

256 
313 

164 
160 

172 
156 

151 
213 

129 

100 


129 
118 
156 

71 

78 

242 
114 

118 

91 
103 

77 
116 

231 
321 

173 
158 

166 

186 

161 

215 

? 
105 


91 


Edinburgh 


113 


Dublin (registration 
area) 


140 


Sydney 


76 


Melbourne 


90 


Montreal 




Toronto 






Paris 

Amsterdam 


162 

203 

209 

208 
156 

301 
340 

279 
222 

196 

218 

244 
212 

156 

185 


103 
64 


Rotterdam 


79 


Stockholm 


82 


Christiania 


107 


St. Petersburg 

Moscow 


249 
333 


Berlin 


142 


Hamburg 


130 


Vienna 


149 




139 


Budapest 


141 


Trieste 


184 


Milan 


102 


Buenos Aires 


96 



INFANT MORTALITY IN DIFFERENT PLACES 351 

If we take the different cities of the United States we shall 
find ranges of infant mortality almost as great as in the cities 
of different countries. In 1915 the New York Milk Com- 
mittee made an extensive study of the infant mortality rates 
of 144 United States cities. The minimum, median and 
maximum rates for the year 1915 were as follows: 



TABLE 104 
INFANT MORTALITIES IN UNITED STATES CITIES 





Number of 
cities. 


Infant mortality. 


Population group. 


Minimum. 


Median. 


Maximum. 


(1) 


(2) 


(3) 


(4) 


(5) 


600,000- 

200,000-500,000 

100,000-200,000 

50,000-100,000 

30,000- 50,000 

20,000- 30,000 


10 
20 
16 
31 
31 
21 


82 
53 
47 
62 
31 
37 


104 

84 
100 
98 
86 
98 


120 
133 
182 
193 
185 
167 



These figures indicate that there was little difference in 
the median infant mortality between the large and the small 
cities, but that in the larger cities there was a greater uni- 
formity in the figures. The very low rates as well as the very 
high rates were found in relatively small cities. The in- 
accuracies of the birth registration may account for many of 
these differences. 

We may go even further and take the different wards of a 
single city, and find these same differences. In the twenty- 
five wards of Boston in 1910 the infant mortalities ranged 
from 75 to 210, the median being 117 and the average 122. 
In eleven districts of Johnstown in 1911 the ''absolute infant 
mortality" varied from 50 to 271, the figure for the entire 



352 STUDIES OF DEATHS BY AGE PERIODS 

city being 134. And in the same way we could find differ- 
ences block by block. In any intensive study it is of funda- 
mental importance to find out the geographical location of 
infant deaths. 

Deaths of infants at different ages. — A year is a long 
time in the life of an infant. One can learn no more from a 
study of the infant mortality, when all ages up to one year 
are considered together, than from a study of the general 
death-rate of a community where all deaths from zero to a 
hundred years of age are considered together. It is necessary 
to study the infant death-rate by months, weeks and even 
days. 

The need of such study is obvious. During early life 
many of the deaths are from troubles incident to birth; later 
the question of feeding, and especially of the effect of artificial 
food becomes important. Some of the welfare activities are 
directed towards one end, some towards another. The 
establishment of milk stations, for example, might affect the 
death of weaned babies, but have little influence on babies 
less than a month old. There are many things which will 
occur to the reader which will show the importance of this 
specific information. 

Let us first consider some of these subdivisions. In doing 
so, we may use several of the methods with which we have 
already become familiar. 

In Hamburg, in 1912, the percentage age distribution of 
infant deaths was as follows: 



DEATHS OF INFANTS AT DIFFERENT AGES 353 



TABLE 105 
INFANT DEATHS AT DIFFERENT AGES: HAMBURG 



Age-group, 
months. 


Per cent of infant 
deaths in group. 


Age, months. 


Per cent of infants who 

died at less than 

stated age. 


(1) 


(2) 


(3) 


(4) 


0+ 


38.5 


1 


38.5 


1+ 


12.3 


2 


50.8 


2+ 


9.8 


3 


•60.6 


3+ 


8.4 


4 


69.0 


4+ 


6.1 


5 


75.1 


5+ 


4.7 


6 


79.8 


6+ 


4.3 


7 


84.1 


7+ 


4.4 


8 


88.5 


8+ 


3.0 


9 


91.5 


9+ 


2.9 


10 


94.4 


. 10+ 


2.6 


11 


97.0 


11+ 


3.0 


12 


100.0 



An irregular grouping is more common, because of the 
greater importance of the subdivisions at the very early ages. 
Thus for Boston, in 1912, we find the following figures: 

TABLE 106 
AGE DISTRIBUTION OF INFANT DEATHS: BOSTON, 1912 



Age-group. 


Per cent of infant 
deaths. 


Age. 


Per cent of infants 

who died at less than 

stated age. 




Male. 


Female. 


Male. 


Female. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


0- days 


15.4 


11.2 


■1 day 


15.4 


11.2 


1+ days 


4.0 


4.5 


2 days 


19.4 


15.7 


2+ days 


3.9 


2.4 


3 days 


23.3 


18.1 


3+ days 


6.8 


7.7 


1 week 


. 30.1 


25.8 


1+ weeks 


3.7 


4.9 


2 weeks 


33.8 


30.7 


2+ weeks 


5.4 


4.4 


3 weeks 


39.2 


35.1 


3+ weeks 


2.8 


2.5 


1 month 


42.0 


37.6 


1+ months 


10.9 


9.0 


2 months 


52.9 


46.6 


2+ months 


7.0 


9.5 


3 months 


59.9 


56.1 


3+ months 


18.1 


19.2 


6 months 


78.0 


75.3 


6+ months 


13.4 


13.6 


9 months 


91.4 


88.9 


9 to 1 year 


8.6 


11.1 


1 year 


100.0 


100.0 


to 1 year 


100.0 


100.0 





354 



STUDIES OF DEATHS BY AGE PERIODS 



It will be noticed that on the basis of the summation 
results of the last column the figures may be readily compared 
with those for Hamburg where the figures are given by 
regular monthly groups. 

The important fact is that the death-rate of infants is 
much higher during the first weeks and days of life than it is 
after the first six months. The apparent increase from the 
eleventh to the twelfth month, often found, is very likely due 
to inaccuracies in stating the age at one year — the error of 
round numbers. 

Specific death-rates of infants at different ages. — A 
better appreciation of the early infant mortality can be. 
obtained by studying the specific death-rates of infants at 
different ages. In Glover's United States Life Tables we 
find the following figures which give the monthly specific 

death-rates. 

TABLE 107 

SPECIFIC DEATH-RATES OF INFANTS BY MONTHS, 1910 

Original Registration States as Constituted in 1900 





Number dying in age interval among 1000 alive at be- 




ginning of age interval. 


Age interval, months. 






Males. 


Females. 


(1) 


(2) 


(3) 


0-1 


48.94 


38.33 


1 + 


13.17 


10.44 


2 + 


10.91 


9.01 


3 + 


9.29 


7.82 


4 + 


8.21 


6.96 


5 + 


7.41 


6.36 


6 + 


6.76 


5.90 


7 + 


6.25 


5.47 


8 + 


5.81 


5.09 


9 + 


5.40 


4.74 


10 + 


5.03 


4.39 


11 + 


4.70 


4.04 


- 1 yr. 


124.95 


103.77 



INFANT MORTALITY BY AGE PERIODS 



355 



Expectation of life at different ages. — The expectation 

)f life is given for infants as follows: 



TABLE 108 
EXPECTATION OF LIFE^ 
Original Registration States as Constituted in 1900 





Average length of life remaining to each one alive at be- 




ginning of age interval. 


Years. 


Age interval, months. 






Males. 


Females. 


(1) 


(2) 


(3) 


0-1 


49.86 




53.24 


1 + 


52.35 




55.28 


2 + 


52.96 




55.78 


3 + 


53.46 




56.20 


4 + 


53.88 




56.56 


5 + 


54.24 




56.87 


6 + 


54.56 




57.15 


7 + 


54.85 




57.41 


8 + 


55.11 




57.64 


9 + 


55.35 




57.85 


10 + 


55.57 




58.05 


11 + 


55.76 




58.22 



1 Based upon deaths in 1909, 1910 and 1911. 

The expectation of life of a male child at birth is about 
the same as that of a 11-year old boy. The expectation of 
life increases from birth to about the third year when it 
reaches its maximum. 

Infant mortality by age periods. — Another way of 
showing the infant mortaUty by age periods is to find the 
ratios between the numbers of deaths in each period and the 
total number of births. These results may also be expressed 
cumulatively. Thus for Boston, in 1910, we have: 



356 



STUDIES OF DEATHS BY AGE PERIODS 

TABLE 109 
INFANT MORTALITY, BOSTON, 1910 



I 



Age period. 


Deaths per 1000 
births. 


Age period. 


Deaths per 1000' 
births. 


(1) 


(2) 


(1) 


(2) 


0-2 days 


20 
12 
16 
21 
21 
17 


0-2 days. . . . 


20 


2 days-1 week 


0-1 week 


32 


1 week-1 month 

1—3 months 


0-1 month 

0-3 months 

0-6 months 

0- 9 months 


48 
69 


3—6 months 


90 


6-9 months 


107 






9-12 months 


15 


0-1 year 


122 



Causes of infant deaths. — In Boston, in 1910, the 
principal causes of infant deaths were as follows : 

TABLE 110 







Number of deaths. 




Male. 


Female. 


(1) 


(2) 


(3) 


I. 


General diseases, total 


113 

16 

18 

8 

10 

15 

11 

47 

21 

18 

4 

209 

37 

88 

79 

355 

25 

320 

2 

8 

2 

69 

392 

302 

9 

35 


100 




Measles 


12 




Diptheria and croup 


8 




Whooping cough 


16 




Erysipelas 


8 




Tubercular meningitis. 


14 




Syphilis 


12 


11. 


Diseases of the nervous system, total . . . 

Meningitis 

Convulsions 


47 

20 
16 


III. 

IV. 


Diseases of the circulatory system, total. 

Diseases of the respiratory system 

Acute bronchitis 


4 
161 

30 




Broncho-pneumonia 

Pneumonia 


71 
56 ♦ 


V. 

VI. 

VIII. 

IX. 


Diseases of the digestive system, totals . 

Diseases of stomach, except cancer. . . . 

Diarrhea and enteritis 

Diseases of genito-urinary system 

Diseases of skin and-cellular tissue 

Diseases of bones, etc 


270 

12 

245 

6 

2 

5 


X. 


Malformations 


51 


XI. 


Early infancy 


319 




Congenital debility 


238 


XIII. 
XIV. 


External causes 

Ill-defined diseases 


7 
32 




Total from all causes 


1245 


1004 



INFANT MORTALITY BY CAUSES 



357 



50 


150 
100 



§50 
o 

o 



p 

S 

(D 
O5O 



S 

a 

^50 




General Diseases Nos, 1-59 



'm7>>^77>^.i^^7Z'>>rl>yf)^(P>>/7^^^ 



Nervous 



Diseases Nos. 60-76 



.»»^^^^^>S..,s>^<^y=7<»?>rr>r^'7777><>r 



r^» r 



Ill-deflne i Diseases 



Nos. 187-9 



50 


50 



All other Diseases 

1908 1909 "" 1910 1911 1912 

Fig. 54. — Infant Mortality by Months, Classified According 
to Cause: Boston, Mass. 



358 STUDIES OF DEATHS BY AGE PERIODS 

Among both male and female infants 37 per cent of the 
deaths were from malformations and diseases of early- 
infancy; about 27 per cent were from digestive diseases; 
about 17 per cent were from respiratory diseases. Together 
the deaths from these causes amounted to four-fifths of all 
the infant deaths. These percentages are not constant. 
There is an important seasonal variation; there are also 
differences according to age and nationality. 

In 1912, Dr. Wm. H. Davis made an excellent analysis of 
the infant deaths in Boston for a five-year period. Fig. 
54, drawn from figures in his report, shows how the 
deaths from digestive diseases have fallen during the sum- 
mer season, but remained almost unchanged during the 
winter; how the deaths from respiratory diseases are 
higher in the winter than in the summer; and how the 
deaths from diseases of early infancy, the general diseases 
and nervous diseases do not have a marked seasonal dis- 
tribution. The diagram also shows how the diseases from 
ill-defined causes have decreased, due, it is said, to better 
diagnosis. 

In Boston the diseases were classified by cause and age 
as follows: 



INFANT MORTALITY BY CAUSES 



350 



• TABLE 111 
CAUSES OF INFANT DEATHS: BOSTON, 1910 





Number of deaths. 


Cause 


3| 


^1 


2| 


m 

in « 

^ o 


03 


CO 

(7) 

58 

24 


89 
112 
2 
2 
3 
3 
8 
1 

15 


IB 

o^ o 




(1) 


(2) 


(3) 

2 

8 

1 

9 

10 







32 

147 



4 

213 


(4 

21 
6 
2 

54 

41 

3 


24 

135 

2 

3 

292 


(5) 

37 

17 

4 

68 

153 

1 





11 

99 

3 

7 


(6) 

43 

17 
1 

80 
201 
2 
3 
2 
7 

12 
4 

33 


(8) 


(9) 


I. General disease 

II. Nervous system 

III. Circulatory system 

IV. Respiratory system . . . 
V. Digestive system 

VI. Genito-urinary system 

VIII. Skin and tissue 

IX. Bones 




1 



1 





41 

305 
5 


353 


52 

21 



69 

108 

3 

2 

2 

2 

5 

1 

5 


213 
94 

8 
370 
625 

8 
10 

7 


X. Malformations 

XL Early infancv 


120 
711 


XIII. External causes 

XIV. Ill-defined causes 


16 
67 


All causes 


400 


405 


317 


270 


'??49 







As would be expected from the definition the largest num- 
)ers of deaths from causes incident to early infancy occur 
imong early infants. This is true also of malformations, 
rhe intestinal diseases reach their maximum effect between 
;he third and fifth pionth, the respiratory diseases and the 
general diseases, which are chiefly communicable, a httle 
ater — say between the sixth and eighth months. 

In Johnstown important differences were noted between 
:he causes of death among infants of native and foreign 
nothers. Thus, during the first year of life the following 
ibsolute infant mortahties, with subdivisions by cause were 
ound. 



360 



STUDIES OF DEATHS BY AGE PERIODS 



TABLE 112 • 
CAUSES OF INFANT DEATHS: JOHNSTOWN 



(1) 



All causes 

Diarrhoea and enteritis 

Respiratory diseases 

Premature births 

Congenital debility or malformations 

Injuries at birth 

Other cause, or not reported 



Native 


Foreign 


mothers. 


mothers. 


(2) 


(3) 


104 


171 


21 


54 


23 


48 


14 


20 


6 


21 


7 


2 


33 


26 



In Boston the following figures were given for 1910 fo 
deaths of infants born to native and foreign mothers: 



TABLE 113 
CAUSES OF INFANT DEATHS: BOSTON 







Rates 


per 1000 births 






9 2 


da 


m 
1— 1 O 

B 


ti'2 


^1 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


Congenital debility and malfor- 
mations 

Diarrhoea and enteritis 


50 
34 

15 

10 

2 

3 


31 
37 

18 

13 

4 

3 


49 
43 

12 

16 

1 

3 


24 
22 

29 
4 
2 

8 


20 
19 


Pneumonia and broncho-pneu- 
monia 

Diseases of early infancy 

Tuberculosis 

Measles, scarlet fever, whooping 
cough and diphtheria. . . .x. . . . . 


16 
7 
2 

4 













THE JOHNSTOWN STUDIES 



361 



The Johnstown studies. — In 1915 the Children's Bureau 
Df the U. S. Department of Labor/ pubUshed an important 
ntensive study of the Infant Mortahty of Johnstown^ an 
ndustrial city of Pennsylvania. Miss Julia C. Lathrop is 
:,he Chief of this bureau. The field work was in charge of 
Miss Emma Duke. This was essentially a sociological 
study. Only a few of the simple correlations can here be 
presented. The report is one which the student may profit- 
ably read in full. 



TABLE 114 
INFANT MORTALITY AND TYPE OF HOME 



Housing condition. 


Infant 
mortality. 


(1) 


(2) 


Clean, dry 


105 
127 

171 

158 

162 
204 

118 

198 

108 
159 


" damp 


Moderately clean, dry 

'* " damp 

Dirtv, dry 


'* damp 


Water supply in house 

Water supply outside 


Water closet 


Yard privy 





Infant Mortality Series No. 3. 



362 



STUDIES OF DEATHS BY AGE PERIODS 



TABLE 115 
INFANT MORTALITY AND SLEEPING ROOMS 





Infant ■ 
mortality. 


(1) 


(2) 


Number of others sleeping in 
same room with baby: 
2 or less 


67 

98 

123 

56 
109 


3 to 5 


Over 5 


Baby sleeping in separate bed: 
Yes 


No 





TABLE 116 
INFANT MORTALITY AND VENTILATION 



Ventilation of baby's room. 


Infant 
mortality. 


(1) 


(2) 


Good 


28 

92 

169 


Fair 


Poor 





TABLE 117 
INFANT MORTALITY AND ATTENDANT AT BIRTH 



(1) 



Physician. 
Midwife . . 



Infant 
mortality. 



(2) 



100 
180 



THE JOHNSTOWN STUDIES 



363 



TABLE 118 

INFANT MORTALITY AND EDUCATION OF 
FOREIGN MOTHERS 





Infant, 
mortality. 


(1) 


(2) 


Literate 


148 

214 
146 

187 


Illiterate 


Speak English 


Do not speak English 



TABLE 119 
INFANT MORTALITY AND AGE OF MOTHER 



Age of mothers. 



(1) 



Under 20. .. 

20-24 

25^29 

30-39 

40 and over. 



Infant 
mortality 



(2) 



137 
121 
143 
136 
149 



The study of feeding was made by months. The following 
figures show the rate of mortality per 1000 babies alive at 
the specified time. 



364 



STUDIES OF DEATHS BY AGE PERIODS 



TABLE 120 
INFANT MORTALITY AND FEEDING 





Specific infant mortality (absolute) 


Age. 


Breast feeding 
only. 


Mixed feeding. 


Artificial feed- 
ing only. 


(1) 


(2) 


(3) 


(4) 


Second month 


72 

54 

•47 
38 
26 
29 
26 
18 
14 


78 

92 . 

57 

40 

32 

22 

20 

16 

11 


237 


Third " 


217 


Fourth " 


166 


Fifth " 


127 


Sixth " 


92 


Seventh " 


72 


Eighth " 


53 


Ninth " 


25 


Tenth " 


11 







In the early ages the difference between deaths of breast 
fed infants and those artificially fed is very great, but th 
difference becomes less as the baby grows older. 



TABLE 121 
INFANT MORTALITY AND HOUSEHOLD DUTIES 



Household duty. 


Infant mortality. 


(1) 


(2) 


Cessation of duties before confinement: 

None or less than one month 

One or more months 

Time of resuming all household duties after con- 
finement: 
8 days or less 


137 
113 

169 
165 
117 


9 to 13 days 


14 days or more 



OTHER STUDIES OF THE CHILDREN'S BUREAU 365 



TABLE 122 
INFANT MORTALITY AND EARNINGS OF FATHER 



Annual earnings of husband. 



(1) 



Under $521 . . . 

$521 to $624... 
$625 to $779... 
$780 to $899... 
$900 to $1199.. 
$1200 or more. 
Ample 



Infant mortality. 



Native wives. 



(2) 



146 
70 

131 
76 



78 



Foreign wives. 



(3) 



251 

162 
130 
167 
152 



108 



The report also contains statistics relating to reproductive 
listories of the mothers studied during the investigation. 

Other studies of the Children's Bureau. — Besides the 
Johnstown studies, here emphasized because they were first 
made, the Children's Bureau has made at this writing (1918), 
intensive studies in Manchester, N. H., Saginaw, Mich., 
Waterbury, Conn., Brockton and New Bedford, Mass., Ak- 
ron, Ohio, and Baltimore. A brief account of these most 
important intensive investigations, based on a first-hand 
collection of the facts may be found in the Quarterly Publica- 
tion of the American Statistical Association.^ 

Two tables from this report are of interest: 

1 Robert M. Woodbury, Infant Mortality Studies of the Children's 
Bureau, June 1918, pp. 30-53. 



366 



STUDIES OF DEATHS BY AGE PERIODS 



TABLE 123 

INFANT MORTALITY AND FATHER'S EARNINGS, 
BALTIMORE 



Earnings of father per 
year. 


True infant 
mortality rate. 


Earnings of father per 
year. 


True infant 
mortality rate. 


(1) 


(2) 


(1) 


(2) 


No earnings 

Under $450 

$450-$549 

550- 649 

650- 849 

850-1049 


207.7 
156.7 
118.0 
108.8 
96.06 
71.5 


$1050-1249 
1250-1449 
1450-1849 
1850 and more 
Not reported 
All classes 


66.6 
74.0 
86.3 
37.2 
140.2 
103.5 



TABLE 124 

INFANT MORTALITY AND ORDER OF BIRTH — MOTHERS 

OF ALL AGES 



Number of birth 
in order. 


True infant mortality. 


Number of birth 
in order. 


True infant mortality. 


(1) 


(2) 


(1) 


(2) 


1 

2 
3 

4 
5 
6 


115.8 
102.7 
111.5 
127.0 
129.3 
132.2 


7 

8 

9 

10 

11 


128.2 
162.6 
142.1 
181.1 
146.8 



Although in general the average infant mortality is less for 
the second child than for the first or subsequent children, 
this is a matter which varies somewhat with the age of the 
mother. For mothers under twenty the mortality is lowest 
for first children; for mothers aged 30-34 years it is lowest 
for the third children; and for mothers aged 35-39 it is 
lowest for fourth children. Perhaps, if nationality were 
considered, other differences would be noticed. 



MATERNAL MORTALITY ^ 367 

Infant mortality problems. — There are many practical 
problems relating to infant mortality which must be studied 
,vith the aid of statistics. The object of the tables here 
riven is to show the complexity of the problem and the 
"utility of depending alone upon the current approximate 
nethod of stating infant mortality. Extensive compilations 
3f data for various places and for different years make easy 
reading and give one a superficial knowledge of the subject, 
but they do not help us very much in solving real problems. 
It is the intensive studies which count. What kind of wel- 
fare work deserves the largest appropriations ? The answer 
depends upon where the babies are dying, at what age they 
are dying, under what social conditions, under what remedi- 
able conditions, and so on. Are the milk stations of our large 
cities a paying life-saving agency? The answer cannot be 
told by comparing the conventional infant mortality rates; 
perhaps the reduction of infant mortality may be among the 
earhest weeks of life, an age at which artificial feeding is less 
common. What relation is there between density of popu- 
lation and infant mortality? The answer cannot be found 
without splitting up the infant mortality into its constituent 

parts. 

■ The lesson is one which the author wishes to teach in every 
chapter of this book, namely, that the vital statistician must 
train himself to analyze his statistics ; to be specific ; to think 
first what kind of facts he needs in order to answer a specific 
question and then go after them, remembering that a small 
number of well-directed statistics are worth more than vast 
numbers of general statistics, piled together without regard 
to internal differences which may make them worthless. 

Maternal mortality. — Closely associated with infant 
mortality we have the problem of maternal mortality. 
Since the long-ago studies of Dr. Oliver Wendell Holmes, 
but especially since the rise of bacteriology, there has been 



368 



STUDIES OF DEATHS BY AGE PERIODS 



a very great decrease in death-rates from child-bed fever 
but even within very recent years we can see an addec 
improvement, which can be attributed to the general at- 
tention being given to pre-natal care, to laws in regard tc 
mid-wives and similar causes. The following condensec 
figures for New York city ^ illustrate this decrease. 



TABLE 125 
MATERNAL MORTALITY-RATE, CITY OF NEW YORK 



Quinquennial 
period. 


Rate per 100,000 females (age 
15-45). 


Puerperal 

sepsis. 


Other deaths. 


(1) 


(2) 


(3) 


1898-1902 
1903-1907 
1908-1912 
1913-1917 


25.9 
26.1 
18.3 
15.3 


40.5 
41.3 
35.7 

29.8 



These figures might more properly have been based on 
married women within the given ages, or upon births and 
still-births taken together instead of on all females of child- 
bearing age, but the chronological differences are so great 
as to leave no room for doubt as to the main facts. 

Childhood mortality. — The period of life between the 
ages of one and five years represents a peculiar environment 
which may be described by the words home and play. In 
this period the physiological influence of the mother on the 
child becomes less, but her intelligence, her social and 
economic condition, the general environment of the house 
and the neighborhood become greater. During these four 
years the specific death-rate of children decreases greatly and 
the diseases to which they are subject change in character. 
1 Weekly Bulletin, Dept. of Health, March, 1918. 



DISEASES OF EARLY CHILDHOOD 



369 



TABLE 126 
SPECIFIC DEATH-RATES OF CHILDREN ^ 
U. S. Registration Area, 1910-1915 





Rate per 1000 


Age. 






Male. 


Female. 


(1) 


(2) 


(3) 


— 1 year 


125.8 


101.1 


1+. 


27.3 


25.0 


2 + 


11.0 


10.1 


3 + 


6.9 


6.3 


4 + 


5.1 


4.7 


0-5 years 


36.0 


30.0 


5-9 


3.3 


3.0 


10-14 


2.3 


2.1 



1 From Dr. Dublin's paper. 

The diseases which occur during childhood are especially 
amenable to preventive measures, a fact which makes their 
study one of especial importance from the standpoint of Hfe 
saving. 

Diseases of early childhood. — Dr. Louis I. DubHn, 
Statistician of the Metropolitan Life Insurance Company 
has discussed these diseases in an article on the Mortality of 
Childhood/ from which the figures for proportionate mortal- 
ity given in Table 127 are taken. 

This table gives only those diseases for which the propor- 
tionate mortality was more than 3 per cent of all deaths. 
One rather unexpected cause of death looms large in this 
table — namely, burns. In the second year of life the 
proportionate mortality was 1.7 per cent, the next year 4.3 
per cent, the next 5.9 per cent, the next 5.7 per cent. Dr. 

^ Quarterly Publications, Am. Statistical Assoc, March, 1918, p. 921. 



370 



STUDIES OF DEATHS BY AGE PERIODS 



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1 



MORTALITIES DURING SCHOOL AGE 



371 



Dublin in the paper referred to gives the specific death-rates 
as well as the proportionate mortalities. The figures for 
burns are for the second year 44.1 per 100,000, for the third, 
44.8, for the fourth, 39.4, for the fifth, 28.1. The increasing 
importance of such communicable diseases as diphtheria, 
whooping cough, measles and the like during this period 
shows the increasing influence of environment and associa- 
tion of children with each other. 

Proportionate mortalities during school age. — During 
the ages from 5 to 15 when children are at school we have 
what is perhaps the maximum opportunity for contact 
infection. During these ages, therefore, we may expect to 
see communicable diseases coming to the front in our pro- 
portionate mortalities. But we also find weaknesses in the 
human mechanism making themselves felt. Tuberculosis 
and typhoid fever also begin to loom up as great menaces. 



TABLE 128 

PROPORTIONATE MORTALITY 

U. S. Registration Area, 1910-15 



Ages 5-9. 


Per 

cent. 


Ages 10-14. 


Per 
cent. 


(1) 


(2) 


(3) 


(4) 


Diphtheria and croup 

Scarlet fever 

Pneumonia 


15.8 
7.1 
5.->9 
4.4 
4.4 
3.7 
3.5 
3.5 
3.4 
3.4 
2.7 
2.6 
2.5 


Tuberculosis of lungs. . . . 
Organic diseases of heart. 
Typhoid fever 


10.2 
8. '6 
6 4 


Organic diseases of heart. . . 

Vehicular accidents 

Tjiphoid fever 


Appendicitis 

Diphtheria 

Pneumonia 

Drowning 


6.3 
5.6 
5.3 


Broncho-pneumonia 


4.4 


Tuberculosis of lungs 

Appendicitis 


Vehicular accidents 

Scarlet fever 


4.4 
3.0 


Tuberculous meningitis .... 

Burns 

Drowning 


Acute -articular rheuma- 
tism 


3.0 


Measles 









372 



STUDIES OF DEATHS BY AGE PERIODS 



Proportionate mortalities at higher ages. — The following 
statistics show the proportionate mortalities for age-groups 
30-34, 50-54 and 70-74 years. 



TABLE 129 
PROPORTIONATE MORTALITY 

U. S. Registration Area, 1914, Males 



Age 30-34 years. 




Age 50-54 years. 




Age 70-74 years. 


^8 


(1) 


(2) 


(3) 


(4) 

13.4 
11.7 
11.0 
8.1 
8.0 
7.7 
6.8 
3.2 
2.9 
1.7 
1.5 
1.4 
1.4 
1.2 


(5) 


(6) 


Tuberculosis 

Accidents 


32.0 
16.1 
6.9 
5.4 
5.2 
4.2 
4.1 
2.8 
2.8 
1.9 
1.6 


Tuberculosis 

Organic diseases of heart 

Bright's disease 

Cancer 

Accidents 

Pneumonia 

Apoplexy 

Suicide 

Cirrhosis of liver ....... 

Diabetes 

Paralysis 

Acute endocarditis 

Pleurisy 

Alcoholism 


Organic diseases of 

heart 

Bright's disease 

Apoplexy 

Cancer 

Pneumonia 


31 6 


Pneumonia 

Organic diseases of heart 
Angina pectoris 


13.4 
12.8 

8.4 
4 9 


Bright's disease '. . . 

Typhoid fever 


Diseases of arteries . . . 
Accidents 


4.5 

3 9, 


Tuberculosis 


?, 8 


Appendicitis 


Old age 


9 


Cancer 


Broncho-pneumonia. . . 
Diseases of prostate. . . . 
Paralysis 


1 9 




1.7 
1 6 




Cirrhosis of liver 

Diabetes . . '. 


1 5 






1 5 




Angina pectoris 

Influenza 


1.4 

9 









Tuberculosis stands at the head of the list until age 70. 
Organic diseases of the heart increase with age. Accidents 
diminish. Bright's disease increases. Suicide decreases. 
Cancer increases, and so on. 

Of course in a complete study all of these diseases at 
different ages should be studied by the use of specific rates 
as well as proportionate mortality. Studies by . sex, by 
season, by nationality, and so on, should also be made. 

Average age of persons living. — The average age of a 
community is, of course, the weighted average of the differ- 



MEDIAN AGE OF PERSONS LIVING 373 

ent age-groups. It is the sum of the ages of all the people 
divided by the total population. 

In 1880 the average age of the aggregate population of 
the U. S. registration area was 24.6 years, in 1890 it was 
25.6, in 1900, 26.3 years. There has apparently been an 
increase although the figures do not stand for exactly 
the same areas. But this result might be due to a les- 
sening of the birth-rate, to an increase in infant mortal- 
ity, to an influx of immigrants of middle age or to a 
reduced death-rate among the aged. That the native 
birth-rate has been declining is true, that immigrants 
of middle age have been entering the country is also 
true. These would tend to increase the average age. But 
the infant mortality has been decreasing, not increasing, 
and the mortahty in the higher age-groups has rather in- 
creased than diminished. These factors would tend to 
decrease the average age. Evidently the problem is so 
compUcated that the average age of the living cannot be 
fairly taken as an index of hygienic conditions. 

Median age of persons living. — Instead of finding the 
average age of the living the median might be used, but 
the objections to the average age of the living would apply 
also to the median, although the magnitude of their in- 
fluence would be somewhat different. The median age of 
the population of the United States has greatly increased 
during the last century as the following figures show: 



374 



STUDIES OF DEATHS BY AGE PERIODS 

TABLE 130 
MEDIAN AGE OF POPULATION: UNITED STATES 



Year. 


Median 




age. 


1800 


16.0 


1810 


16.0 


1820 


16.5 


1830 


17.2 


1840 


17.9 


1850 


19.1 


1860 


19.7 


1870 


20.4 


1880 


21.3 


1890 


21.9 


1900 


23.4 


1910 


24.4 



Average age at death. — Nor does the average age at 
death afford a fair index of the healthfulness and physical 
welfare of a community. The reasons are similar to those 
just mentioned. A high average age at death may mean 
simply that the birth-rate is low. 

There has been, in recent years, a general rise in the 
average age at death. In Rhode Island, for example, tlie 
increase has been as follows: 



TABLE 131 
AVERAGE AGE AT DEATH: RHODE ISLAND 



Period. 


Average age at 
death. 


Period. 


Average age at 
death. 


(1) 


(2) 


(3) 


(4) 


1861-65 
1866-70 
1871-75 
1876-80 


29.32 
32.42 
30.16 
31.21 


1881-85 
1886-90 
1891-95 
1896-00 


33.99 
33.42 
33.96 
34.53 



EXERCISES AND QUESTIONS 375 

In 1900 the average age at death in the registration 
states of the U. S. was 36.8 years. For the cities it was 
32.4; for the rural districts 44.7 years. In Mass., in 1910, 
the average age at death was 39.51. In 1913 the average 
age at death for the U. S. Registration Area was 39.2 years 
for males, 40.6 years for females, and 39.8 years for the 
entire population. 

In a general way, however, the prolongation of life may be 
regarded as an index of human progress, as Professor W. F. 
Willcox has pointed out. 

EXERCISES AND QUESTIONS 

1. Compare the infant mortalities for certain assigned large cities 
and rural districts. 

2. Compare the infant mortalities for California cities with those of 
eastern cities. 

3. Compute the seasonal variations of infant mortality for Cali- 
fornia cities. 

4. What is the average infant mortality in New South Wales? Why 
is it so low? 

5. Do the statistics of infant mortality justify the continuance of 
the milk stations in New York City? 

6. In what direction will efforts to reduce infant mortality yield the 
most profitable results? 

7. Is poverty, ignorance, race or climate the greatest factor in causing 
high infant mortalities? 

8. Make a statistical study of some cause of death, to be assigned by 
the instructor, according to age periods. 



CHAPTER XII 
PROBABILITY 

In the second chapter it was shown that the average, or 
mean, of a number of figures gave a very inadequate idea of 
the figures themselves; that two sets of figures may have the 
same average yet differ among themselves in a striking 
manner. . It is often important to find out what these differ- 
ences, or variations, are. '-We have seen that one way to do 
this is to arrange the items in array, that is, in order of 
magnitude and find the median, the mode, the quartiles and 
so on, but even this is not enough;' it is necessary, if possible, 
to find some mathematical relation between the variations. 

Natural frequency. — It is a curious and important fact 
that if we measure natural objects, such as the lengths of the 
leaves on a tree, or the heights of a regiment of men, or the 
lengths and breadths of nuts, to use illustrations studied by 
the Eldertons in their Primer of Statistics, we shall find that 
most of the observations will be very close to the mean of all, 
that a few will differ from it considerably and that a very 
small number will differ from it very greatly. In a thousand 
observations a certain number are almost sure to differ from 
the mean by a definite amount, and a certain other number 
are almost sure to differ from the mean by twice that amount. 
In fact these relations are so regular as to amount to what 
may be called a law of nature, a sort of natural frequency. 
In these variations we shall find some observations larger 
than the mean and some smaller. Natural frequency can 
best be understood by an example. 

376 



NATURAL FREQUENCY 



377 



In a certain army the results of measurement of the 
heights of 18,780 soldiers were as follows: 



TABLE 131 
HEIGHTS OF SOLDIERS. 



Height in inches. 


Number of soldiers. 


Per cent of soldiers. 


(1) 


(2) 


(3) 


60 + 


197 


1.05 


61 + 


317 


1.69 


62 + 


692 


3.69 


63 + 


1,289 


6.86 


64 + 


1,961 


10.44 


65 + 


2,613 


13.91 


66 + 


2,974 


15.84 


67 + 


3,017 


16.07 


68 + 


2,287 


12.18 


69 + 


1,599 


8.52 


70 + 


878 


4.67 


71 + 


520 


2.77 


72 + 


262 


1.39 


73 + 


174 


0.92 


Total 


18,780 


100.00 







It will be seen that the mode, the most commonly observed 
height, was in height-group 67+, i.e., 5 feet 7 inches and 5 feet 
8 inches. The mean was 67.24 inches. If we should at- 
tempt to stand these 18,780 in array we should have an 
impossible task. We might try it, however, and obtain 
something like this : 

There are 18,780 soldiers in all. The middle one would be 
number 9390, or between this and 9391. By counting up 
from the left we find that the median is just a little below 67 
inches. There are, of course, differences in height in each 
group and with care we could get the median exactly. By 
taking a weighted average, as described in the second chapter, 
we could get the mean. But just now we are interested in 



378 



PROBABILITY 



the variations. We can plot the number of soldiers by height 
groups, as in Fig. 55. This will give us a characteristic 
curve highest in the middle and sloping downwards gently 









i 








J 






y 
























\ 


\ 








\ 



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o 



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w 

o 



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m 

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o 



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02 



bO 
O 






M 



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towards either end. This is called a frequency curve. It 
should be noticed that whereas in the array the height was 
indicated by the vertical scale it is in this diagram indicated 
by the horizontal scale. 



WHAT IS MEANT BY "CHANCE" 



379 



Coin tossing. — Ten coins were tossed into the air by the 
students in one of my classes an aggregate of 1250 times, 
records being kept of the number of heads which came up. 
The results were as follows : 



TABLE 132 
RESULTS OF COIN TOSSING 



Number of heads 
up at once. 


Number of throws. 


Number of heads 
up at once. 


Number of throws. 


(1) 


(2) 


(1) 


(2) 




1 

2 
3 
4 
5 


1 

15 

62 
156 
265 

288 


6 
7 
8 
9 
10 


266 

128 

55 

13 

1 



These results when plotted gave a frequency curve which 
was much like that obtained for the soldiers. This curve 
was evidently the result of chance. One cannot tell for any 
given throw how many heads will come up, yet in the long 
run we always get some such result as that obtained by the 
coin tossing students. 

What is meant by '* chance. '* — What determines 
whether a coin thrown into the air will fall with the head up ? 
Many things, of course, — the way it is held when thrown, 
the twist with which it starts, the height to which it rises, 
the manner in which it strikes the floor, the way it rolls, and 
many other factors. The sum total of these many causes 
gives what we call '' chance." Chance is not the absence of 
cause, it is the result of a multiplicity of causes. In chance 
we must judge the result by the combination of these many 
causes. Often it is the only way we can judge the result. 
In chance we can never tell exactly any particular result, 



380 PROBABILITY 

but we can form an idea as to the frequency with which any- 
possible result will occur. 

In the case of the coins we could not tell in advance the 
result of any particular throw of ten coins but we could safely 
predict that five heads would be thrown more often than any 
other number, and that no heads or ten heads would happen 
least frequently. Is there any way by which the frequency 
that other numbers of heads would be thrown can be ascer- 
tained? There is, and it is quite simple. 

We will start with a single coin. We toss it up. It is an 
even chance as to whether it comes up a head or a tail. If 
we should toss the coin a hundred times we would probably 
have a head in fifty of the throws. In practice it might not 
come out exactly 50, it might be 48 or 55, but if we tossed 
the coin an enormously large number of times a head would 
come up half the time. Let us now take two coins which 
we will call a and h. If we indicate a head by heavy type 
then we have the following possible combinations: 

ab; ab; ab; ab. 

We thus have the following results: 

Heads 1 2 

Number of throws 12 1 Total 4 

If we have three coins we have the following possible 
chances : 

abc; abc, abc, abc; abc, abc, abc; abc. 

Heads 12 3 

Number of throws 13 3 1 Total 8 

If we have four coins we have : 

abed; abed, abed, abed, abed; abed, abed, abed, abed, 
abed, abed; abed, abed, abed, abed; abed. 

Heads 12 3 4 

Number of throws 14 6 4 1 Total 1^ 



BINOMIAL THEOREM 



And so it goes on until for 10 coins we have: 



381 



Heads 01 2 3 4 5 6 789 10 

Number of throws 1 10 45 120 210 252 210 120 45 10 1 Total 1024 

Theoretically, therefore, the coins in 1250 throws should 
have given us the following numbers: These compare rea- 
sonably well with those obtained by the students. 



TABLE 133 
THEORETICAL RESULT OF TOSSING 10 COINS 1250 TIMES 



Number of heads. 


Number of throws. 


Number of heads. 


Number of throws. 


(1) 


(2) 


(1) 


(2) 





1 


6 


257 


1 


12 


7 


147 


2 


55 


8 


55 


3 


147 


9 


12 


4 


257 


10 


1 


5 


354 







Binomial theorem. — Another interesting fact is that 
these numbers which we have just obtained as representing 
what would result from applying the laws of chance to the 
tossing of two, three and more coins, are the same as are 
obtained by expanding the sum of two quantities by the 
binomial theorem, (a + h)"^ in which each quantity, a and h 
is taken as 1, i.e., (1 + 1)". In the problem a head was just 
as Hkely to come up as a tail. In this expression n is the 
number of coins. If 



n = 1, 


(1 + 1)' 


= 1 + 1, 


n = 2, 


(1 + ly- 


= 1 + 2 + 1, 


n = 3, 


(1 + D' 


= 1+3 + 3 +1, 


n = 4, 


(1 + D* 


= 1 + 4 + 6 +4 +1, 


n = 5, 


(1 + 1)=' 


= 1 + 5 + 10 + 10 + 5 + 1 



382 PROBABILITY 

The binomial theorem, therefore, gives us a method of 
finding the shape of any natural frequency curve if we know 
the number of terms. It should be observed that only^ the 
even values of n give an odd number of terms with a middle 
highest term. 

Some interesting conclusions may be predicted from this 
application of the binomial theorem. One of them is that 
the larger the number of terms the more closely are the 
items clustered around the median figure. It follows that 
the average of a large number of observations is much more 
precise than the average of only a few observations. In 
fact, it can be shown that the error of a set of observations 
varies inversely as the square of the number of observations. 
If we multiply the number of observations by four, we halve 
the probable error. 

Chance and natural phenomena. — Does it follow there- 
fore that the measurements of natural phenomena result 
from chance ? Certainly, if they follow the binomial law as 
pointed out. How is it in the case of the heights of soldiers? 
Here we had 18,780 soldiers. Theoretically, these should 
have been distributed as shown in Column 3. Actually they 
were distributed as in Column 2. The differences are yery 
slight. 

What are the many causes which determine a person's 
height? It is difficult to say. Possibly inheritance, age, 
nationality, food supply during the period of growth, early 
iUnesses, habits of sleeping, sitting, standing and many other 
factors. It would be an interesting subject for discussion. 
Whatever the causes are they are combined in so many ways 
that we have no better method of predicting the heights of 
the soldiers in a regiment than by the application of this 
law of chance. 



SKEW CURVES 



383 



TABLE 134 
HEIGHTS OF SOLDIERS 





Per cent of soldiers. 


Height in inchea. 








Actual. 


Theoretical. 


(1) 


(2) 


(3) 


60 + 


1.05 


1.00 


61 + 


1.69 


1.71 


62 + 


3.69 


3.68 


63 + 


6.86 


6.75 


64 + 


10.44 


10.51 


65 + 


13.91 


13.99 


66 + 


15.84 


15.84 


67 + 


. 16.07 


15.31 


68 + 


12.18 


12.60 


69 + 


8.52 


8.84 


70 + 


4.67 


5.31 


71 + 


2.77 


2.67 


72 + 


1.39 


1.18 


73 + 


0.92 


0.61 




100.00% 


100.00% 



Skew curves. — In plotting natural phenomena it will be 
found that not all frequency curves are symmetrical. The 
median is not always the mean; there may be more items on 
one side of the mean than on the other. The asjrmmetrical 
curves are known as skew curves. They are not susceptible 
of mathematical analysis except by the use of complicated 
and rather uncertain methods. 

There are four common types of asymmetrical curves 
commonly met with in demographic studies. . These are 
shown in Fig. 56. In this diagram A represents the sym- 
metrical frequency curves, the two sides of which are sym- 
metrical about the mode. This type of curve has already 
been discussed. Type B is represented by the age distribu- 
tion of deaths from measles. In early childhood the curve 



384* 



PROBABILITY 



rises sharply. Type C \a a, variant of B. Type D starts off 

with the mode and steadily 
diminishes. Age distribu- 
tion of infant deaths by 
months gives us an example 
of this curve. Type E, the 
U-shaped curve, is already 
familiar to us. It is sub- 
stantially the ciKve of spe- 
cific death-rates by ages. 
All of these skew curves 
take many forms. 

It will be remembered 
that in the case of the law of 
chance it was assumed that 
the chance of an event 
happening and of its not 
happening were equal. The 
chance of the coin falling 
as a head was the same as 
that of its falling as a tail, 
and one or the other was 
bound to happen. But we 
can imagine a result de- 
pending upon many factors, 
one of which was much more 
likely to occur than not to 
occur. This would result 
in producing a skew curve. 
There might be many such 
factors, and these might exist 
in all sorts of combinations. 
When statistics naturally 
plot out as a skew curve it 




TYPE E U-SHAPED 

Fig. 56. — Types of Frequency 
Curves. 



DEVIATION FROM THE MEAN 385 

is a sign that they should be investigated to determine, if pos- 
sible, what the influence is which is producing the skewness. 
Sometimes it can be found. For example, in a case recently 
studied the quantity of butter fats in a series of analyses 
of milk samples was slightly skewed at one end. This was 
found to be due to the adulteration of about five per cent 
of the samples with water. 

Beyond recognizing the skewness of a curve and making 
some attempt to account for it, the student of vital statistics 
will do well to let the mathematics of skew curves alone. 
Karl Pearson and others of his school have suggested certain 
methods of mathematical analysis. 

Frequency shown by summation diagrams. — Another 
way of expressing '^frequency" is by the use of the summa- 
tion, or cumulative, diagram. In some respects this is more 
useful than the method of plotting by separate groups. Let 
us return to our 18,780 soldiers whose heights were measured. 
If 197 soldiers were between 60" and 61" then 197 were 
less than 61"; if 317 were between 61" and 62" then 197 + 
317, or 514, were less than 62"; and so on. If these results 
are plotted we shall obtain a characteristic ogee curve. If 
the distribution is exactly in accordance with the law of 
natural frequency then the upper and lower parts of the 
curve will be symmetrical. 

Instead of using the actual numbers of soldiers beginning 
with 197 and running up to 18,780, we might have plotted 
the percentage distribution from 1.05 per cent to 100 per cent. 
The result would have been the same. 

Deviation from the mean. — Still another way of study- 
ing these figures is to find the extent to which the heights of 
the soldiers differed from the average, or mean, height. The 
mean height was 67.24". For the sake of simplicity let us 
call it 67i". We may fairly assume that the height measure- 
ments were measured accurately and that the average height 



2 • 



386. PROBABILITY 

of the 197 seldiers in height group 60'' — 61" was 60 
Then the average deviation of the height of these 197 soldiers 
from the mean was 67i — 60J, or 6|". In the same way the 
317 soldiers had an average deviation of 5|; and so on. 
The average deviation of group 73 — 74" was 73^ — 67i or 
6i. Some of these deviations are positive and some are 
negative, because some of the soldiers are shorter than the 
mean and some are taller. 

If we plot these results we obtain the curve shown in 
Fig. 57. This is the curve of error, so-called. The deviations 
from the mean are regarded as errors. It is similar to the 
summation curve of variation. In fact it is the same curve, 
the only difference being the scale. Mathematicians, physi- 
cists and engineers look at their data from the standpoint of 
errors of observation, and therefore their text- books which 
treat of this subject are called ^^ Precision of Measurements," 
''Theory of Least Squares," and the like. Natural scientists 
however speak of '^ Variation." It is all one. The figures 
show us that small errors occur very often, large errors occur 
less frequently, and very large errors rarely occur. 

In any set of measurements we may assume that errors 
will exist, and that in natural phenomena there will be varia- 
tions caused by many factors. We are naturally interested 
to find out the extent of these variations. We want to know 
the average deviation and the variation most likely to occur. 
It will not be possible to go into these matters in great detail 
in this book. Readers who want to know the theory of these 
matters must study the theory of probability, or "Least 
Squares." A few methods of dealing with the subject 
practically will be given because they have an important use 
even in elementary statistics. In doing so we will consider 
first a very simple set of figures, and then come back to some 
more measurements of men, but lest we tire of our 18,780 
soldiers we will consider some more recent measurements 



STANDARD DEVIATION 



387 



made by Drs. Frankel and Dublin of the Metropolitan Life 
Insurance Company. 

Standard deviation. — Let us suppose that we have five 
figures, or statistics, which represent something, no matter 





6 




















j 


c 

t-H 










J 












J 










/ 


% 


















y^ 




a 

o 
^5 




y 








fl 9 

O " 

.2 
6 




X 








/ 


/ 








/ 





















20 



40 60 

Per cent of Soldiers 



80 



100 



Fig. 57. — Percentage Deviation of the Heights of Soldiers from 

the Mean. 



what. They are 6, 8, 2, 4, 5. The mean of these figures is 
5. The deviations from the mean are respectively 1, 3, —3, 
The average deviation, disregarding signs, is 



— 1, and 



388 



PROBABILITY 



their sum divided by 5, or 1.6. A more useful quantity is 
that called the standard deviation. It is obtained by squaring 
these deviations, finding the average square and taking its 
square root. If we average the data in tabular form we shall 
better understand the process. 



TABLE 135 
STATISTICAL DATA 



I 



Item. 


Deviation from 
Mean. 


Square of 
Deviation. 


(1) 


(2) 


(3) 


6 
8 
2 
4 
5 


1 

3 
-3 

-1 



1 

9 
9 
1 



Sum 25 
Ave. 5 


8^ 
1.6 


20 
4 



1 Neglecting signs. 

The average square is 4 and Vi is 2. Hence 2 is the standard 
deviation. It will be noticed that the standard deviation 
gives greater weight to the large deviations than a mere 
averaging of the deviations does. 

Coefficient of variation. — The ratio between the stand- 
ard variation and the mean is called the coefficient of varia-^ 
tion. In the case just mentioned it is 2 -^ 5, or 0.40. The 
coefficient of variation is usually expressed decimally -v If 
the variations are very small the coefficient of variation is 
small. If the variations are large the coefficient of variation 
is large. In some parts of the country the annual rainfalls 
do not vary much from year to year. In Massachusetts the 
coefficient of variation is about 0.17. In other parts of the 
country there are great fluctuations from year to year. In 



COMPUTING THE COEFFICIENT OF VARIATION 389 

Arizona the coefficient of variation is 0.50. A low coefficient 
means, in general, that the figures are more dependable; a 
high coefficient means that they are likely to be untrust- 
worthy because of their fluctuations. This coefficient is 
very useful in the study of vital statistics. 

Computing the coefficient of variation when data are 
grouped. — This is likely to cause trouble to the beginner. 
It is necessary to use care or mistakes will be made. Sup- 
pose we have the following items divided into magnitude 
groups between and 5, the measurements being made to 
the nearest tenth as shown in columns (1) and (2). 



TABLE 136 
STATISTICAL DATA 



Magnitude 
group. 


Number in 
group. 


Average 
magnitude. 


Product. 


Deviation 

of number 

in group. 


Square of 
deviation. 


Product. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


0-0.9 
1-1.9 
2-2.9 
3-3.9 
^^4.9 


6 
8 
2 
4 
5 


0.45 
1.45 
2.45 
3.45 
4.45 


2.70 
11.60 

4.90 
13.80 
22.25 


1.76 

0.76 

-0.24 

-1.24 

-2.24 


3.10 
0.58 
0.06 
1.54 
5.02 


18.60 
4.64 
0.12 
6.16 

25.10 


Total 


25 




55.25 
2.21 






54.62 


Mean 








2.18 















Here we first find the average magnitudes of the numbers 
in each group, column (3). By multiplying these by the 
number of items in each group and dividing by the number 
of items we have (4) the weighted average, or the mean of all 
the items. This is 2.21. Subtracting the figures in column 
(3) from 2.21 we have the. group deviations in column (5). 
These are squared (6) and then multiplied by the number of 
items in each group (7) . The sum of the squares divided by 
25 gives the average square, i.e., 2.18 and V2.18 is 1.48, the 



390 PROBABILITY 

standard variation, 1.48 -^ 2.21 gives 0.67 the coefficient 
of variation. Unthinking students sometimes multiply the 
figures in column (5) by those in column (2) before squaring. 
This is wrong. It is the deviations which are squared. The 
subsequent process is merely to get the weighted average of 
the squares. 

Probable error. — Neither the average deviation from 
the mean nor the standard deviation is the one most likely 
to occur. It is the median deviation, or the median error, 
which is most hkely to occur. It can be shown by calculus 
that when observations follow the normal law of error, or 
the normal frequency distribution, i.e., the binomial dis- 
tribution, the median deviation is about two-thirds of the 
standard deviation. To be exact, the figure is 0.6745. If 
we let r stand for this median deviation, this probable error, 
and if we let x be any individual error, and if n = the number 
of observations, then, remembering that the sign S means 
'Hhe sum of," we shall see that 



V n 



r = 0.6745 

n 



This is merely the mathematical way of stating what we 
have just done. Xx^ means the sum of all the squares of the 

deviations, -^- means the average square, and y — means 

the square root of the average square, i.e., the standard 
deviation. Where does 0.6745 come from? If we take the 
curve of error (Fig. 57), and consider the side to the left of 
the middle ordinate, it will be possible to draw a vertical line 
somewhere to the left (or the right) of the middle which will 
divide the area included between the curve and the base line 
into two equal parts. The height of the ordinate which will 
do this is 0.6745 that of the middle ordinate. 



THE PROBABILITY SCALE 391 

This probable error is quite useful in statistics. One use 
is that of throwing out of. consideration doubtful observations. 

Doubtful observations. -^Scientists make a distinction 
between errors and mistakes. Errors are supposed to fall 
within the limits of probability; mistakes are supposed to be 
glaring, erratic observations which really ought to be left 
out of account, or at least not included when the average is 
computed. We have all had experiences of this kind. In 
a daily record of the number of bacteria in a filtered water 
we may find that where most of the figures are less than 25 
per cubic centimeter there is one which exceeds 1000. Shall 
we include this in the average for the month ?. If we do we 
unduly raise the average for the month and bring discredit 
on the filter. And yet there may be no reason for excluding 
it. It may have been a fact. And a fact is not to be dis- 
carded. 

The theory of probability gives us a means of telling 
whether it should be included in the average or not. If we 
know the probable error r, as above described, then we shall 

find that there is an allowable ratio of - which depends upon 
the number of observations. If we had only three obser- 
vations then any value of the ratio - which is greater than 
about 2 should be regarded as outside the probable variations 

X 

resulting from the law of chance. If n is 10 the limit of - 

r 

X 

is 3; if n = 30, then the limit of - is 3.5; if n is 100, the limit 

is 4; if n is 500, the limit is 5, and so on. These values are 
merely approximate. 

X 

The probability scale. — This ratio of -, the ratio of any 

error to the mean, or most probable error, is useful in another 
way because on the basis of the binomial distribution we can 



392 



PROBABILITY 



compute the frequency with which any value of - is Hkely to 

occur. We call this the probability of its occurrence. 

If X is any error and r is the most probable error then when 

- = 1 the chances are even that the error will be x. There 

r 

are as many chances that the error will be larger than x as 

that it will be smaller. We may call this a ''fifty-fifty" 

chance, and we may write the probability of its occurrence 

as i or 0.5. If - is less than 1 the probability that any error 
r 

will be less than - is less, and if - is greater than 1 the prob- 

T r 

X 

ability that any error will be less than - is greater. In fact 
we shall find that the following relations hold: 



TABLE 137 
PROBABILITY 



X 


Probability that any 


X 


Probability that any 


r 


error will be less than • 
r 


r 


error will be less than - • 
r 


(1) 


(2) 


(1) 


(2) 


0.0 


0.0000 ) 


1.7 


0.7485 


0.1 


0.0538 


1.8 


0.7753 


0.2 


0.1073 


1.9 


0.8000 


0.3 


0.1603 


2.0 


0.8227 


0.4 


0.2127 


2.1 


0.8433 


0.5 


0.2641 


2.2 


0.8622 


0.6 


0.3143 


2.3 


0.8792 


0.7 


0.3632 


2.4 


0.8945 


0.8 


0.4105 


2.5 


0.9082 


0.9 


0.4562 


2.6 


0.9205 


1.0 


0.5000 


2.7 


0.9314 


1.1 


0.5419 


2.8 


0.9410 


1.2 


0.5872 


2.9 


0.9495 


1.3 


0.6194 


3.0 


0.9570 


1.4 


0.6550 


4.0 


0.9930 


1.5 


0.6883 


5.0 


0.9993 


1.6 


0.7195 . 


CX) 


1.000 



PROBABILITY PAPER 



393 



X 



If we compute the values of - which correspond to certain 
probabihties we have the following approximate figures: 

TABLE 138 
PROBABILITY 



Probability. 


I 

r 


Probability. 


X 

r 


(1) 


(2) 


(1) 


(2) 


0.01 


0.02 


0.80 


1.90 


0.02 


0.04 


0.90 


2.44 


0.03 


0.06 


0.95 


2.91 


0.05 


0.09 


0.98 


3.45 


0.10 


0.19 


0.99 


3.82 


0.20 


0.38 


0.999 


4.887 


0.30 


0.58 


0.9999 


5.783 


0.40 


0.77 


0.99999 


6.592 


0.50 


1.00 


0.999999 


7.258 


0.60 


1.25 


0.9999999 


7.967 


0.70 


1.54 







Probability paper. — Until recently it has been difficult 
to use the theory of probability in statistical work, but it is 
now easy/ In 1913, my partner, Dr. Allen Hazen, devised a 
new kind of plotting paper. The percentage scale was so 
spaced that any set of figures which follow the natural law 
of probability would plot out not as an ogee curve, but as a 
straight Une. The spacing was based fundamentally on the 
preceding figures, but it was necessary to take account of 
the sign of the error, whether positive or negative, and make 
allowance for this in designing the plotting paper.- The 
50 per cent, or median fine, was placed in the middle of the 
percentage scale. The other relative distances were as fol- 
lows. The figures given cover only one side of the 50 per 
cent line. 



394 PROBABILITY 

TABLE 139 
DATA FOR PREPARING PROBABILITY PAPER 



Line. 


Relative dis- 
tance. 


Line. 


Relative dis- 
tance. 


Line. 


Relative dis- 
tance. 


(1) 


(2) ■ 


(1) 


(2) 


(1) 


(2^ 


Per cent. 




Per cent. 




Per cent. 




50 


0.000 


17 


1.415 


0.8 


3.573 


48 


0.074 


16 


1.474 


0.7 


3.646 


46 


0.149 


15 


1.537 


0.6 


3.727 


44 


0.224 


14 


1.602 


0.5 


3.821 


42 


0.300 


13 


1.670 


0.4 


3.933 


40 


0.376 


12 


1.742 


0.3 


4.077 


38 


0.453 


11 


1.818 


0.2 


4.267 


36 


0.531 


10 


1.906 


0.1 


4.585 


34 


0.611 


9 


1.988 


0.09 


4.630 


32 


0.693 


8 


2.083 


0.08 


4.685 


30 


0.777 


7 


2.188 


0.07 


4.748 


28 


0.864 


6 


2.305 


0.06 


4.817 


26 


0.954 


5 


2.439 


0.05 


4.900 


24 


1.047 


4 


2.596 


0.04 


5.000 


22 


1.145 


3 


2.789 


0.03 


5.120 


20 


1.248 


2 


3.045 


0.02 


5.290 


19 


1.302 


1 


3.450 


0.01 


5.550 


18 


1.357 


0.9 


3.507 







As first used the percentage scale was used horizontally, as 
in Fig. 63. There are some advantages plotting the per- 
centages as ordinates as in Figs. 58, 59 and 60. 

In the latter the horizontal scale is the ordinary arithmet- 
ical scale. The vertical scale may be labeled from to 100 
per cent, in either direction, or it may read from to 50 on 
either side of the median line. It depends upon whether we 
want to keep the positive and negative errors separate or add 
them together and consider their magnitude alone. 

A few examples of the use of this probability paper will 
now be given. 

For a more complete description of this paper the reader 
is referred to the author ^s monograph on the *' Element of 
Chance in Sanitation." ^ 

\Jour. Franklin Institute, July, 1916. 



PROBABILITY PAPER 



395 



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= = = ^ = ... = .z.......J = = = = . = r = . ..... = = = . = = .: = =. = .:=.::. = ..........-.... ........^ 99 


_-_^ ^ 


" - [ . 


: i: T 1 


:^:::::: 


1 _I 


--/ --- 99 9 


=---- j___ = 






I " ± ""■" " " "" : --- _ _ ___ 


^r 


L _ 99 99 


55 GO 65 70 15 80 
Height- in inchea. 



Fig. 58. — Distribution of Soldiers According to Height, 
on Arithmetic-Probability Paper. 



Plotted 



396 



PROBABILITY 



•55 Bi 



3 
bo 



& 



.-tJ a 



99.99 



99.9 



99 

95 
90 

80 
70 
60 
50 
40 
30 
20 

10 



0.1 



0.01 







1 






:::::::::::::: ::::^::.^^ 












/ 













i 






1 n/H-H 
r— 






T ^ 






— . , ,. - ^ 






1-. -- 







• _^ 






::::z:: ::::?::::::;:::=::=:::::::::::; ::i::::::: 
EEEEE ::;::?:EE:EEE:EE:EEEEE:EEEEE;EEEEE=:E=====^E 

::::::::^::::::::::::::::::::: :::::::::: :::::::::: 






»' — 

iiliEiiiE^Ei:::;:::;!::;;:!;;^;;;;;;^^::::^ 




:::::::::::::::: 


r^EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE 
) 




\mmim 


:::;:::::::::||:::|::::::::::::::::::::::::::^ 




?_ __ - 






4- 






^-] 






r' 

/ 






.-I 






lilzzzzlzz^zlll 


.-]-- — 11 1 1 '"1 M 1 1 1 1 1 1 1 1 


/ 


1 




/ 






/ 












/ 






i 







0.01 



0.1 



10 





1^ 


20 


w 8 


30 


Xi n 




U V 


40 


f| 


50 


•9 «> 


60 
70 


II 
21 




o <1> 




■M M 


80 


»< 9. 



10 



14 18 22 

Death Rates per lOQD 



26 



90 



95 



99 



99.9 



99.99 



Fig. 59. — Death-rates of Massachusetts Cities and Towns. 
Plotted on Arithmetic-ProbabiUty Paper. 



PROBABILITY PAPER 



397 



"1 1 




: ~ t .' : "- -.. 


::::;.::::::::::;-:::: x j 


= = = EEEnEEEaMEEln==HM=im = l==EE = = EEE =pd^ 


I — ^ :""tf ""::::::::::: 


J ^ 


— J fj^ 


- - - - ..:kj 


: TcSv 


'" " " " - iJ-^oS, 


:::::i:::: :::_:_: .._ ...-___-___------.^L^^-_-_-, -___--__-_ -_._._-^ 


---.--. -- 435 t. -It 

.„._.. J../ z.. 




' " ^t f J^ 




It L ' / * 


:::::::::::::: ;: f-i. : : :: '^tir.z ::: :~::; 


... . — _ _ — 1 1 V ^ ^ 




/ y / 


I 1 o. '\y\ 


:::z:::::= =" = = "::: :ii::z::i== = -::izii"i:J:^i:::""S^^":i"-:::i::::i:ir: 


z::::z:-:::z::::iz:iiizzzz:-zi:z:iizzizzzzf-bi:zzzz^^?:zz:zzzzzzzzzzzz::::i 


^ :--- :-::::::::::::::::::::::::: 1 ::::::-?.::::::::::::::: ::::::::::' 


- f j' - - - 


J , v*^ - 




- : __ ; tt ,2 : ; 




— -t " 3a ,2 : ; 






_;; : i i : , 










:::::::::ii;ii;;;i;: -:::_:-:: ;:ii:iiii#-::--------.--.-_-----^ 


















>f i :.~ ,; 










llX----------------------^ — ------t^--- ---------- - — ----"----^^ ! 


EEEEEEEEEE EEEEEEE EEEEEE^^EE E EE EE=^ EEE EEE EEEEEEEEEEEEEEEEEEEnEEEEEEEEEE^ 










.__:.:_:__: ^ ■*___: :„:-f: L; ^ : 


r 5- 3 : : :---:-:--:-:-::-:* 




,^ ':,:.:: : 


/'::::: / _._ ___ 


_:_:::_: y. A.j _ < 


y - - / - 


; ::::;.?::: . ., 


..../. li 


V ...J..L _ _.. 


3_._: - — - 




: -..; : :j.:_. : :_ 


::::/::::::::: — ::::::::: :: . .. .. : 


... / i . - 


. _ / ' 


,L. 


:=======;:=======_= _=3===i-r=_"==_===_=__===_==-===r_=====r-=r_r_=-r_=_zr;;;=- 












i . 



90 



110 



100 
Per cent of Median. 

Fig. 60. — Percentage Variation of Death-rates of Massachusetts 
Cities and Towns for Three Different Decades. Plotted on 
Arithmetic-Probability Paper. 



39S PROBABILITY 

Examples of use of probability paper. — Fig. 58 shows 

the distribution of soldiers according bo height plotted on 
probability paper. This is based on the observations with 
which we have already become familiar. It will be noticed 
that instead of forming the usual ogee curve the points 
fall on a straight line. 

Fig. 59 shows that the death-rates for Massachusetts 
cities and towns also plot out on this paper as a straight 
line. Fig. 60 shows that in 1900-10 the death-rates 
throughout the state have been more uniform than in 
1860-70. This is indicated by the different slope of the lines. 

For an example of the use of logarithmic probability, 
paper, see Fig. 63. 

Another use of probability. — Bernouilli's theorem gives 
us another interesting application of the theory of probability. 

If we let p represent the frequency of an event happening 
and g the frequency of its not happening, then obviously 
p -\- q = 1. Unless this fundamental condition holds, the 
laws of probability do not hold. It is always well to see if 
there are any other factors than p and q. 

If we let n represent the number of cases considered, and 
€ the mean error, then Bernouilli says, e = v ?^pg. We need 
not stop here to prove this, but we may see how it can be 
used. If n is large then e is a fair measure of the deviation 
from the standard for it is said that in 2 out of 3 cases the 
deviation will be less than e; in 19 out of 20 cases less than 
2 e; and deviations greater than 4 e are very rare. 

Let us suppose that in a population of 10,000 the 

general death-rate was 15 per 1000, i.e., 150 deaths in all. 

15 985 

Then n = 10,000; p = j^ ; q = j^; then 



sjio, 



1 f: qqk 

000 X -^ X -^ = V147.75 = 12.15 deaths, 
1000 1000 ' 



THE FREQUENCY CURVE AS A CONCEPTION 399 

or 1.2 per 1000. A fluctuation of this amount from year 
to year would not be outside of the bounds of chance phe- 
nomena. If the population were 1,000,000 then e would be 
Vl.4775 or 1.2 deaths in 1,000,000 or 0.012 per thousand. 

Other criteria than Bernouilli's have been suggested for 
this computation. The results differ considerably, and none 
of the methods must be taken as mathematically exact. 

Let us suppose we are studying an epidemic of typhoid 
fever in which all the cases, 120, were actually caused by the 
public water supply. The population was 50,000. There 
were two milk dealers: A served 40,000 persons; B served 
10,000 persons. What would be a chance distribution of 
cans among these two dealers? If they were distributed 
uniformly we should expect to find among A's customers 

-^' ^„ of 120, or 96; and among 5's customers .,^' ^^ , or 24. 
oU,UUU oUjUUU 

Now what is a reasonable variation from these figures? In 

the case of A, 



J.^r^r.^ 120 49,880 ,^ . ^ , 

€ = y 40,000 X ^^-^ X ^QQQQ = 10 approximately. 

Therefore, if A had any number between 86 and 106 it would 
be within the bounds of chance. • If he had 116 cases it 
might be a suspicious circumstance. In the case of B, 



= Y 10,000 X ^^T^AA ^ ^nnnn = ^.4 approximately. 



120 49,880 
50,000 ^ 50,000 



If, therefore, B had more than 27 cases it would be suspicious. 
The frequency curve as a conception. — The frequency 
curve is something far beyond a statistical tool. Prop- 
erly conceived it stands for a universal principle. Not all 
the leaves of a tree are alike, not all shells are alike, sol- 
diers are not all of the same height or weight. We cannot 
well compare the tallness of pine trees and elm trees with- 



400 PROBABILITY 

out resorting to the frequency curve. One man may say, 
'' The ehn tree is the taller; I have seen elms taller than 
pines." Another says, " That is nothing; pine trees have 
a greater average height." But the first man is not con- 
vinced. He goes back to his own observation and insists 
that he has seen elms taller than pines. To give the true 
picture both men need to know the frequency of different 
heights of both elms and pines. 

Are young women as good scholars as young men? 
Assuming that we have an adequate definition of what is 
meant by a good scholar, can we settle the question by 
saying that we have seen young women who were better 
scholars than young men, or that the average of scholar- 
ship is higher among men; must we not know the fre- 
quency with which we find good scholars and poor scholars 
among both men and women? It is quite conceivable 
that among women we have greater extremes of scholar- 
ship than among men, or vice versa. 

Are women as well fitted for voting as are men? Suffra- 
gists point to drunken sots and say, " We are better fit tec 
to vote than they are." When they say this they are com- 
paring the end of one frequency curve with the middle oi 
the upper end of the other. Such comparisons are utterly 
meaningless. 

Sometimes we need to make comparisons on the basis 
of lower limits, sometimes on the basis of upper limits 
sometimes we ought to compare modes, sometimes medians 
sometimes averages, sometimes we do not know the facti 
well enough to make comparisons at all: but through 
out all realms of thought an appreciation of the funda 
mental importance of the frequency curve will help us t( 
reason soundly and will prevent us from making fals« 
comparisons. 

The frequency curve contains in itself the element o 



THE FREQUENCY CURVE AS A CONCEPTION 401 

beauty. Moons wax and wane; the tide rises and falls; 
the flowers of spring come, first a few, then many; and they 
disappear in the same way, a few hngering into summer. 
It is said that we Uve in a world of chance. Nothing is 
more true. We live in a world where many causes are 
acting with and against. each other. We live in a world of 
frequency curves. Artists and architects recognize this. 
The ogee curve is the line of beauty. 

EXERCISES AND QUESTIONS 

1. Find data for and plot an example of a typical symmetrical fre- 
quency cm*ve. (Anthropometrical measurements.) 

2. Find data for and plot an asymmetrical frequency curve (specific 
death-rates for scarlet fever, diphtheria, etc.). 

3. Describe the application of Bernouilli's Theorem to the chance 
distribution of cases among milk customers? [See Am. J. P. H., Apr.^ 
1912, p. 296.] 

4. Construct a model to illustrate the general law of probability.- 
[See Rosenau's Preventive Medicine, Chapter on Heredity and Eu- 
genics.] 

5. Repeat the coin tossing experiment described in this chapter. 

6. Find the height of 50 males (or females) above eighteen years of 
age, and compute: 

a. The average deviation from the mean. 
6. The standard deviation. 

c. The coefficient of deviation. 

d. The probable error. 

7. Plot the height records of these persons on "probability paper." 

8. Discuss the use of the law of chance in public health studies. 
(Whipple, Geo. C. The Law of Chance in Sanitation, Jour. Franklin 
Institute, July, 1916.) 

9. Prepare a short statistical abstract of the stature of recruits, 
U. S. A., 1906-15. [Hoffman, Frederick L. Army Anthropometry 
and Medical Rejection. Newark. Prudential Press, 1918.] 



CHAPTER XIII 
CORRELATION 

4 

Correlation is the word by which the statistician describes 
the correspondences or relations between series, classes or 
groups of data; in fact, it is largely for the study of these 
relationships that statistics are collected. 

Deaths from typhoid fever are arranged by months in 
order to ascertain if there is a fixed relation between the 
frequency of such deaths and the season of the year; or they 
are arranged by the age, occupation or place of residence of 
the decedants in order to learn of any other correspond- 
ences which may exist. The heights and weights of men, 
or women, are compared to see if the variations in height are 
related to variations in weight; the length of the arm is 
compared with some other measurement of the body; the 
heights of sons are compared with the heights of their fathers. 
These are all simple correlations. Two sets of measurements 
only are compared. 

Often the problem is more complicated. The infant 
mortality in cities varies with the season, being highest in 
the summer; the temperature of the air also varies with the 
season, being highest in the summer; and the statistician 
desires to ascertain if there is any definite relation, any 
correlation, between atmospheric temperature and infant 
mortality. Here there are three elements to be considered — • 
season, temperature and infant mortality. Also the number 
of flies ordinarily increases with an increased atmospheric 
temperature, and the question arises "Is there a fixed re- 

402 



CAUSAL RELATIONS 403 

lation between the increase in the number of flies and 
the infant mortaUty?" One naturally asks: "Why not 
eliminate the temperature of the air and study the direct and 
simple correlation between flies and mortality? That 
would, indeed, be the best and safest method, but unfortu- 
nately the data may not exist, or cannot be obtained in 
comparable form. It is, therefore, necessary to devise some 
way of studjdng this problem by indirect correlation, or 
secondary correlation. 

Causal relations. — Sometimes statistics are studied 
merely to determine whether correlation exists between two 
variables, this result being practically useful. The knowledge 
that infant mortality increases with the atmospheric tem- 
perature is in itself of value to the physician and the health 
officer. More often perhaps the underlying motive in corre- 
lation studies is that of determining cause and effect. In 
the illustration given the question is. Is the increase in 
atmospheric temperature the cause of the increased mor- 
tality among infants ? Is the increase in the number of flies 
in the summer the cause of the increased infant mortality? 
Or, to go back to the examples of simple correlation, Is the 
increased height of men the cause of their increased weight? 
Is the tallness of a son the effect of the tallness of his father ? 
Does the establishment of correlation also mean that a 
causal relation has been established? To answer this we 
must consider what is meant by cause. 

Jevons ^ says: ''By the cause of an event we mean the 
circumstances which must have preceded in order that the event 
should happen. It is not generally possible to say that an 
event has one single cause and no more. The cause of the 
loud explosion in a gun is not simply the pulling of the trigger, 
which is only the last apparent cause or the occasion of the 
explosion; the qualities of the powder, the proper form of 
^ Lessons in Logic, p. 239. 



404 CORRELATION 

the barrel; the existence of some resisting charge; the proper 
arranging of the percussion cap and powder; the existence 
of a surrounding atmosphere, are among the circumstances 
necessary to the loud report of the gun; any of them being 
absent it would not have occurred." In the above phrase, 
"the circumstances which must have preceded in order that 
the event should happen," emphasis must be placed on the 
word must, otherwise our reasoning is post hoc non propter 
hoc. 

r^It is obvious that statistics do not in themselves establish 
these causal relations. The laws of logic are the primary 
laws, and the rules of statistics must be subsidiary to them. 
Westergaard, the celebrated Danish statistician, has recently 
said (Jour. Am. Stat. Asso., Sept. 1916, p. 259), ''that the 
task of the statistician is not so much to find the causality 
himself as to help others to find it. The statistician must be 
content if he can show that certain groups of numbers have 
marked]differences, leaving it to physiology, meteorology and 
other sciences to explain these differences."" 

The statistician can prove nothing by his statistics unless 
he uses them logically. 

On the other hand, the statistical arrangements of facts 
are of the greatest aid in helping to establish causal relations, 
because by expressing facts by numbers it is possible to con- 
centrate extended experiences into quantities which may be 
easily and quickly compared. 

Correlation and causality. — In studying correlation as 
a process for determining causality it is necessary to dis- 
tinguish between the simple correlation which may exist 
between two variables and the more indirect correlation, or 
secondary correlation, which occurs when two series of events, 
both correlated to a third factor, are compared to each other. 
The former may be safely used to establish a causal relation; 
in fact, King says (Elements of Statistics, p. 197), that 



LAWS OF CAUSATION 405 

"correlation means that between two series or groups of 
data there exists some causal relation." In stating this he 
evidently had in mind the simple correlation between two 
variables. And, of course, ''causal relation" does' not mean 
''sole cause." Besides correlation we must also establish 
connection between the two variables. It is not the task of 
the statistician to do this. It would be more exact to say- 
that a causal relation may he shown hy establishing a definite 
correlation between two series, classes or groups of connected 
data. 

It is chiefly in secondary correlations that we err in our 
logical processes. In mathematics we learned that '^two 
things which are equal to a third are equal to each other," 
but it is not necessarily true that two series of events which 
vary as a third are equal to each other, or even are related to 
each other at all. Infant mortality increases with the 
atmospheric temperature in summer; the softness of the 
asphalt pavements increases with the atmospheric tempera- 
ture in summer; but we cannot infer that there is any 
relation between infant mortality and the softness of asphalt 
pavements. 

The actual connection between events is not shown by 
statistics or by the statistical methods except as the data are 
interpreted according to the laws of logic. 

Let the reader try to answer questions hke these. Why 
is it not true that there is a causal relation between the soft- 
ness of pavements and infant mortality? Is it, or is it not, 
true that there is a causal relation between the presence of 
flies and infant mortahty? Which shows the higher degree 
of correlation with infant mortality — the presence of flies 
or the softness of asphalt? 

Laws of causation. — While we are thinking about cor- 
relation and its relation to causation it will not be out of 
place to refer to the three methods of induction as stated 



406 CORRELATION 

by John Stuart Mill. The cause of an event may be said 
to be '' the circumstances which must have preceded in 
order that the event should happen." 

Mill's first canon is, '^ If two or more instances of the 
phenomenon under investigation have only one circum- 
stance in common, the circumstance in which alone all the 
instances agree is the cause (or effect) of the given phe- 
nomenon." This is the method of agreement. The epi- 
demiologist follows this principle when he studies case 
after case of disease looking for some common antecedent 
circumstance. Here one instance does not establish proof 
of a cause, and the larger the number of instances the 
stronger the proof. 

The second canon is ''if an instance in which the phe- 
nomenon under investigation occurs, and an instance in 
which it does not occur, have every circumstance in com- 
mon save one, that one occurring only in the former; the 
circumstances in which alone the two instances differ is 
the effect, or the cause, or an indispensable part of the 
cause, of the phenomenon. This is the method of differ- 
ence, the method of experiment. This principle also is 
used in epidemiology. 

The third canon is called the joint method. *' If two or 
more instances in which the phenomenon occurs have only 
one circumstance in common, while two or more instances 
in which it does not occur have nothing in common save 
the absence of that circumstance; the circumstance in* 
which alone the two sets of instances (always or invariably) 
differ, is the effect, or the cause or an indispensable part 
of the cause, of the phenomenon." 

These are sometimes expressed as follows, the large let- 
ters, A, B, C, etc., representing antecedents, and the small 
letters, a, h, c, etc., the consequents. 



METHODS OF CORRELATION 407 

Method of Agreement 

ABC ah c 

A D E ade 

AF G af g 

A H K ahk 



Method 


of Difference 


ABC 




ah c 


B C 




h c 


Joint Method 




ABC 




ah c 


AD ^E 




ade 


AF G 




af g 


AHK 




ahk 


P Q 




pq 


R S 




r s 


T V 




t V 


X Y 




X y 



Methods of correlation. — Correlations may be divided 
into two classes: — (1) simple, or primary, and (2) secondary. 

Simple correlations are studied as between two variables, 
these two variables being compared on the basis of magni- 
tude, that is they are compared by grouping. 

Secondary correlations are studied when two variables are 
compared with each other after first being compared to a 
third variable — such as time or place. 

When two variables are so correlated that the numerical 
values increase and decrease together the correlation is said 
to be direct. 



408 CORRELATION 

When the correlation is such that the numerical value of 
one variable increases as that of the other decreases the 
correlation is said to be inverse. 

The closeness of correlation is termed the degree of correlation. 
There are mathematical methods of determining the degree 
of correlation, according to which perfect correlation is repre- 
sented by unity and complete absence of correlation by zero. 

The following are some of the methods used in the study 
of correlation: 

Simple correlations (two variables compared directly) : 

1. Plotting of Original data. 

2. Correlation table (grouping by lines and columns). 

3. Correlation model (correlation surf ace) . 

4. Plotting of group means (Galtori). 

5. Computation of coefficient of correlation: 

(a) Galton's method (see Elderton's Primer of 

Statistics) . 
(h) Karl Pearson's method. 

6. Use of mathematical formulae. 

Secondary correlations (two variables compared on the 
basis of a third variable) : 

1. Comparisons between two plotted lines representing 

original data, as to: 
(a) Parallelism, 

(6) Correspondence of fluctuation in time of oc- 
currence and in magnitude, 
(c) Correspondence of cycles. 
{d) Lag. 
(e) Inverse relations. 

2. Comparison between two plotted lines, each represent- 
ing variations from the mean. 

3. CojQparison between two plotted lines, each represent- 
ing variations from the moving average (or some smoothed 
line showing trend) . 



GALTON'S COEFFICIENT OF CORRELATION 409 

Galton's coefficient of correlation. — Let us suppose that 
we have the following pairs of observations. Each a has a 
corresponding h. What is the correlation between a and 6? 
Offhand one can see that in a general way a and h rise and 
fall together. But how can we express this relation? 

TABLE 140 
EXAMPLE OF CORRELATION 



a 


h 


X 


X2 


y 


V- 


xy 


(1) 


(2) 


(3) 


(4) 


(5) 


■ (6) 


(7) 


7 
5 
6 
3 
9 


4 

2 
5 

1 
8 


-\ 



-3 

3 


1 
1 


9 
9 




-2 
1 

-3 
4 



4 

1 

9 

16 



2 

9 
12 


Sum 30 
Average 6 

(T 


20 
4 




20 
4 
2 




30 
6 
2.45 


23 
4.6 











We cannot compare the figures directly. We do not even 
know that the measurements are the same, a may be 
expressed in feet, and b may mean years or something else. 
What have these two sets of figures in common? The 
deviations from their means may help us. Let us suppose 
that X represents the deviation of a from its mean, 6, and 
that y stands for the deviations of h from its mean, 4. 
Then we can compute the standard deviation of each set 
of figures, and call these ax and ay. These we find to be 
Vi, or 2, and V6, or 2.45. We must now link together the 
two sets of observations and we do this by finding the prod- 
ucts of their deviations, i.e., xy, and the average of xy, i.e., 
4.6. This average value of the product of x and y, divided 
by the product of the standard variations, ax and ay, gives 
what Galton calls the coefficient of variation. It may be 
expressed by formula thus: 



410 



CORRELATION 



Coefficient of correlation = 



TKJxOy 



in which n is the num- 



ber of observations, and l^xy the sum of all the x^/'s. 



example, 



2x2/ 23 



= -^ = 4.6, and the coefficient 



IS 



In the 
4.6 



^ ^ _._, „ 2 X 2.45 

= 0.94. This is a close correlation between a and 6, because 
1 represents perfect correlation and no correlation at all. I 

Pearson's coefficient is not quite the same, but it is enough 
for practical purpose to remember Galton's. 

Example of low correlation. — In the monthly bulletin 
of the Connecticut State Department of Health for Feb., 
1918, a radial diagram is given showing that grippe out- 
breaks in one year are followed by measles the next year, 
and the statement is made that 'Hhe wheel of chance becomes 
a wheel of certainty." Let us see if these facts will stand 
the test of correlation. If we place the deaths from grippe 
in one year side by side with the deaths from measles the 
following year, we have the following twelve pairs of values 

for a and 6. 

TABLE 141 



a 


h 


X 


Z2 


2/ 


y1 


zy 


a) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


8 
4 

15 

11 
6 
8 

16 
7 

12 
2 
9 

25 


32 
8 

26 
5 
6 

22 

3 

27 

12 
6 

34 


-2.25 
-6.25 

4.75 

0.75 
-4.25 
-2.25 

5.75 
-3.25 

1.75 

-8.25 

-1.25 

14.75 


5.06 
39.06 
22.56 

0.56 
18.06 

5.06 
28.06 ■ 
33.06 

3.06 
68.06 

1.56 
217.56 


16.92 

- 7.08 

- 9.08 
9.92 

- 9.08 
-13.08 

4.92 

-12.08 

11.92 

- 3.08 

- 9.08 
18.92 


286.29 
50.13 
82.45 
98.41 
82.45 

171.09 
24.21 

145.93 

142.09 

9.49 

82.45 

357.97 


-38.07 
+44.25 
-43.13 
+ 7.44 
+38.59 
+29.43 
+28.29 
+39.26 
+20.86 
+25.41 
+11.35 
+279.07 


Sum 123 
Average 10.25 
O" 


181 
15.08 




441.72 

36.81 

6.07 


1532.96 

127.75 

11.30 


442.75 











CORRELATION SHOWN GRAPHICALLY 411 

It will be seen that the coefl&cient of correlation is 
i:xy 442.75 



na^ay 12x6.07x11.30 



= 0.54. 



This is a low correlation. It is less than the coefficient of 
variation of either grippe or measles. It follows, therefore, 
that the statement that grippe is followed by measles a year 
later has little to substantiate it, if all the facts are considered. 
If we leave out a few exceptional years there does appear to 
be a general tendency for measles to follow grippe. But 
what right is there to leave out some of the facts? If they 
are mistakes they should be left out, otherwise they should 
be considered in drawing concessions. 

A few years ago a sanitary chemist tried to show a relation 
between the color of water and the typhoid fever death-rates 
in Massachusetts water supplies. Computations of the 
coefficient of correlation for 54 places where surface water 
was used gave a figure of 0.16, while for 33 places where 
ground water was used it was 0.30. In other words there 
was very little correlation. In the same cities the correla- 
tions between the general death-rates and the typhoid fever 
death-rates were 0.59 and 0.56, respectively. 

On the other hand, the Eldertons found the coefficient of 
correlation between the length and breadth of shells to be 
0.95; that between the ages of husbands and wives, 0.91. 

The student will find the use of the coefficient of correlation 
an admirable weapon for exploding false theories. 

Correlation shown graphically. — In a general sense any 
graph with horizontal and vertical scales, in which pairs of 
observations are represented by a single point is a correlation 
plot. If the points fall on or near a straight line the correla- 
tion is high; if the points are so scattered that a straight line 
cannot be readily drawn to represent them the correlation 
is low. This needs no further illustration. 



412 



CORRELATION 



It is possiblej however, to determine the coefficient of 
correlation graphically. In Bowley's Elements of Statistics 
we find the relation between the marriage-rate and the price 
of wheat. The first step is to select two suitable scales and 
plot the data as points. The second step is to find the mean 
marriage-rate and the mean price of wheat and plot these as 

17.0 



16.5 



16.0 



^15.5 



15.0 



li.5 



14.0 



























.M 




































/ 




























c 








/a 






































































































00 






































CO 






j 
































;^ 






/ 






































/ 
































^ 




1 


' 
















































































































f 




































/ 






































/ 






































/ 






































/ 






































L 








..R 




m 


»ai 


^ 


15. 


L7. 


■~" 






~" 


■~" 


~^ 




.y 




■"■ 










— ■ 




■^ 




' 
























* 






























/ 






































/ 






































1 






























* 






/ 






































/ 






































t 




































) 






































J 






































L 




































./ 


fN 





























20 



30 40 50 

Price of Wheat, In Shillings 



60 



Fig. 61. — Correlation between Marriage-rate and Price of Wheat. 

horizontal and vertical lines, respectively. The third step 
is to draw a line which will fairly well represent the points. 
In Fig. 61 this line is marked MN. It must pass through 
the intersection of the mean lines, 0. The fourth step is to 
select any point on MN, as, for example. A, and read from 
the vertical scale the value of AB. In the example AB is 
16.7 — 15.17 = 1.53. This is really the deviation of A 



THE CORRELATION TABLE 413 

from the mean marriage-rate and 1.53 ^15.17 = 10.15 is 
the standard variation. In the same way AC is 46.0 — 37.8 
= 8.2, the deviation of A from the mean price of wheat, and 
8.2 -T- 37.8 — 21.7 is the standard variation. The ratio of 
10.15 to 21.7 gives us the coefficient of correlation, 10.15 -^ 
21.7 = 0.468. By computation Bowley finds this to be 
0.47. The graphical method is useful only when the correla- 
tion is fairly high, because if the correlation is low one cannot 
tell where to draw the line MN. In drawing this line an 
effort should be made to place it so that there will be as many 
points as possible near the line, with the other points as well 
balanced as possible on either side of the line. This requires 
experience and a sort of intuitive sense of distances. 

A recent example of lack of correlation. — The Munic- 
ipal Tuberculosis Sanitarium of Chicago, in its annual 
report for 1917, has published an interesting series of 
diagrams illustrative of the lack of correlation between 
housing and tuberculosis. Fig. 62 is one of these. The 
districts are arranged in order of occurrence of tubercu- 
losis. The one-scale rectangles, appropriately divided ac- 
cording to the character of rooms, fail to show any progres- 
sion coincident with tuberculosis under Chicago conditions. 

The correlation table. — The correlation table is arranged 
much like a simple plot. There is a horizontal and a vertical 
arrangement of groups. This tabulation shows to the eye 
the relation between the two quantities. In Table 142 we 
see the correlation between the ages of husband and wife is 
fairly close. Of 669 wives in age-group 40-44, 309 were married 
to husbands in the same age-group. There is a slight tend- 
ency for husbands to be slightly older than their wives. The 
figures are not s^mimetrically arranged around the mode. 

The correlation model is used but little. A description of 
its construction and use may be found in works on statistical 
methods. 



414 



CORRELATION 



-60. 1-600- 

T.B. 

57 



>POP. 



ROOMS 

570 



t.bT 



54 540 



51 

T.B. 



510 

CASES 



Interior Rooms 
^ Side Rooms on o'oo"to 2' 



^s, 



/ " 

Side Rooms on 2 1 to 4 



•;i: ;':-i Court Rooms 

Mid-Year Rooms on 12' or less 



1 




Fig. 62. — Diagram Showing Lack of Correlation between Interior 
Rooms in Certain Chicago Blocks and Tuberculosis Morbidity. 



i 



SECONDARY CORRELATION 



415 



TABLE 142 

CORRELATION BETWEEN (1) THE AGE OF WIFE, (2) THE 
AGE OF HUSBAND, FOR ALL HUSBANDS AND WIVES 
IN ENGLAND AND WALES WHO WERE RESIDING TO- 
GETHER ON THE NIGHT OF THE CENSUS, 1901. 
(CENSUS, 1901, SUMMARY TABLES, P. 182.) TABLE BASED 
ON 5,317,520 PAIRS; CONDENSED BY OMITTING OOO'S 

(From Yule's Theory of Statistics, p. 159.) 



Ages 

of 
hus- 
bands. 


Ages of wives. 


Total. 


15- 


20- 


25- 


30- 

(5) 


35- 

(6) 


40- 

(7) 


45- 

(8) 


50- 

(9) 


55- 

(10 


60- 

(11) 


65- 

(12) 


70- 


75- 


80- 


85- 


(1) 


(2) 


(3) 


(4) 


(13) 


(14) 


(15) 


(16) 


(17) 


15- 

20- 
25- 
30- 
35- 
40- 
45- 
50- 
55- 
60- 
65- 
70- 
75- 
80- 
85- 


2 

16 

4 

1 


2 

173 

185 

41 

9 

3 

1 




























4 

240 

688 

817 

793 

700 

595 

483 

369 

• 277 

175 

104 

50 

18 

4 


46 

402 

265 

69 

17 

6 

2 

1 


4 

84 

411 

251 

71 

20 

8 

3 

1 

1 


1 

10 

84 

369 

219 

66 

19 

8 

3 

1 

1 






















2 

12 

80 

309 

178 

57 

18 

8 

3 

1 

1 


1 

2 

12 

66 

252 

146 

46 

16 

6 

2 

1 


















1 

2 

12 

59 

195 

110 

39 

11 

5 

2 

1 
















1 

2 

10 

44 

141 

81 

26 

8 

3 

1 














1 

2 

10 

35 

101 

53 

18 

5 

1 












1 

2 

6 

23 

58 

31 

10 

2 

1 






















1 

4 

13 

31 

14 

4 

1 












1 
2 
6 
12 
5 
1 












1 
1 
2 
3 

1 


1 




























































Total 


23 


414 


808 


854 


781 


669 


550 


437 


317 


226 


134 


68 


27 


8 


1 


5317 



Use of mathematical formulae. — It is often desirable to 
find the equation of a straight hne or curve drawn through 
a series of points. This is not difficult, but it requires a 
longer description than can be given here. The student 
can find good descriptions of the methods used in standard 
mathematical books. 

Secondary correlation. — The correlation of two variables 
is often shown by plotting each against a third quantity, 
which latter varies in a regular manner. Thus in Fig. 52 we 



416 CORRELATION 

have the number of cases of typhoid fever plotted as ordi- 
nates with months as abscissae, and we have also the atmos- 
pheric temperature plotted as ordinates with months as 
abscissae. Here we see that there is a general correspondence 
between the two curves and we say that there is correlation 
between the two. One must be very careful in using the 
graphic method in this way. We may have a diagram in 
which the correspondence between the two plotted lines is 
very definite except occasionally, yet these occasional lapses 
may be enough to upset the correlation. Again two lines 
may rise and fall together in point of time, and they 
may even rise and fall apparently the same amounts, yet 
this may be an incident depending on the scales used. 
Finally we must not forget that this sort of correlation — 
where two quantities vary as a third — does not establish 
causality. 

In Fig. 53 we have typhoid fever death-rates and popu- 
lation supplied with filtered water, both plotted with time 
as the abscissae; and we notice that as one line goes up 
the other goes down, giving a sort of inverse correspond- 
ence. We are not justified however in calling this a 
close correlation. Certainly we are not justified in saying 
that one is the cause of the other. It may be true, and 
few will dispute the fact that the filtration of polluted 
water tends to reduce the typhoid fever death-rate among 
the consumers of the water, but such a diagram as this 
does not prove it. As Phelps^ says, we might plot] a line * 
showing the increase in the number of telephones which 
would very much resemble that of the population supplied 
with filtered water.'- Pearson does well to call this correla- 
tion based on comparison with a ^'common mutual," a 
" spurious correlation.^' A good many false conclusions 
have been based on statistics treated in this way. 
1 Am. Jour. Pub. Health, 1917, p. 23. 



THE LAG 417 

The lag. — When two lines are plotted with the scale of 
abscissae in common to both variables it often happens 
that one line changes in curvature after the other; it lags 
behind it. Sometimes this lag is very regular, sometimes 
it is more or less irregular. This lag does not necessarily 
show lack of correlation. It may, on the other hand, result 
from cause and effect. It is obvious that a cause must 
precede in time the effect produced by that cause. It may 
require a certain interval of time for the cause to make 
itself felt, and this naturally would produce a lag. For 
example, let us suppose that it takes ten days after a 
typhoid infection for the victim to '^ come down " with the 
disease; then a plotted line showing by days the number 
of cases of typhoid fever would lag behind a line showing 
infection of the water-supply, — if we can imagine such 
facts to be plotted. Conversely, if we had the two plotted 
lines we might compute the length of the incubation period 
of typhoid fever by measuring the lag. If the comparison 
is between the dates of infection and the dates of deaths 
from typhoid fever, then, of course, the lag is much longer 
as it includes not only the period of incubation, but also 
the run of the disease, and this is not the same for all 
persons. 

A device sometimes used is the " set back." If we are 
comparing two curves, one of which is supposed to represent 
the cause of the other, we may plot the causal curve on the 
true dates and we may set back the dates of the resulting 
curve by an amount equal to the lag. Correlation will 
then be indicated by the correspondence of the curves. 
This presupposes that the amount of the lag is known. 

In comparing lagging curves which are apparently correl- 
ative it is important to distinguish between cause and 
effect. As we have reiterated, it is not the function of 
correlation to demonstrate causality. 



418 CORRELATION 

Fig. 52 is an example of the use of the set back. This is 
a correlation between typhoid fever deaths and atmospheric 
temperatures, the deaths being set back two months. 

Coefficient of correlation and the lag. — It is possible to 
deal with the lag analytically instead of graphically. We 
may find that by comparing two series of statistics, date 
for date, the coefficient of correlation is low; by setting one 
series back a day and recomputing the coefficient we may 
find it higher; by setting back two days the coefficient may 
be higher still; and by using greater set backs the coeffi- 
cient may increase to a maximum, and beyond that point 
it may decrease. ^The set back which^produces the highest 
correlation may be taken as a measure of the lag. W 

All such matters as these are fully discussed in the text- 
books of general statistics. 

Other secondary correlations. — Sometimes the second- 
ary character of a correlation is not as clearly revealed as 
in the case of two plotted lines with common abscissae. It 
has been noticed that poliomyelitis cases seem to follow 
the river valleys; what is the real correlation here? It 
does not appear to be a direct correlation. One says that 
fleas are correlated with the river valleys, and that, secon- 
darily, the disease is correlated with the fleas; another says 
that the lines of transportation are along the river valleys 
and that the real correlation is between poliomyelitis and 
the contact of people incident to intercommunication. 

The whole matter of correlation is almost inseparable 
from the science of logic. 

The epidemiologist's use of correlation. — Epidemiology, 
a branch of medical science, is based fundamentally on the 
laws of cause and effect. The epidemiologist is continually 
searching for the cause of outbreaks of disease in order that 
they may be checked and future outbreaks prevented. In 
his studies he uses statistics continually and is of necessity 



THE EPIDEMIOLOGIST'S USE OF CORRELATION 419 

mightily interested in correlation. The successful epi- 
demiologist must have a nose for facts, must be able to 
analyze these facts skillfully and draw logical conclusions 
from them. 

The influence of a particular factor as a cause of disease 
is often studied by means of statistics. For example, the 
filtration of a public water-supply may be followed by a 
reduction of the typhoid fever death-rate among the water 
takers. This is a sort of correlation, — one change being 
followed by another. We know, moreover, by inductive 
reasoning from many such occurrences in the past and also 
from experimental evidence that this is a correlation which 
implies causality. In using this method of reasoning, how- 
ever, it is important to know that the change in the water- 
supply was the only change which occurred. 

There are scores of instances where this method of 
reasoning has been used. In Panama the abolition of the 
mosquito reduced the death-rate from yellow fever. The 
evidence points to this as a clear-cut case not only of cor- 
relation, but causality. In Panama also the malaria has 
been greatly reduced since the anti-mosquito work was be- 
gun. But here we find that quinine has been used as an 
additional preventative. In this case therefore we have had 
two factors changing at about the same time. From ex- 
perimental evidence there is no doubt in regard to the 
causal relations between malaria and the Anopheles mos- 
quito, but statistically the evidence is not as strong as in 
the case of yellow fever. 

In some of the old studies of typhoid fever it was found 
that the death-rate decreased after the introduction of a 
sewerage system. This was accompanied by an abolition 
of house privies. Now it was probably the abolition of 
the old privies, not the building of the new sewers which 
produced the result. In other cases a public water-supply 



420 CORRELATION 

was installed at the same time that the sewers were built. 
A reduction in the typhoid death-rate following these events 
may have been due to either or to both. 

The fact should not be overlooked that when epidemics 
occur there is not infrequently more than a single factor 
involved. Sometimes an outbreak can be traced to a 
single initial case, but just as in lighting a fire the match is 
applied to the paper, the burning paper sets fire to the 
kindling and the burning kindling sets fire to the coal, so a 
single case may start infections which may be scattered in 
various ways. It is important for the epidemiologist to 
find all of these methods of transmission. 

Sometimes the epidemiologist is obliged to base his action 
upon statistics which show correlation without waiting to de- 
termine whether this correlation also means causation. For 
example, in the recent pandemic of influenza a certain vac- 
cine, supposed to have a prophylactic value, was used upon 
several hundred persons. The question arose, ''Shall this 
vaccine be distributed and generally used? " The data first 
collected showed a fair degree of correlation between the use 
of the vaccine and apparent protection against the disease, 
and on the strength of this finding the vaccine was dis- 
tributed. Later studies, however, failed to corroborate the 
correlation at first noticed, and showed that there was no 
causal relation between the use of the vaccine and failure of 
persons to take the disease. It was really a case of correla- 
tion without causation, — post hoc non propter hoc. And yet 
the health authorities, compelled to take action one way or 
the other, were right in basing action on the supposed corre- 
lation. 



EXERCISES AND QUESTIONS 421 

EXERCISES AND QUESTIONS 

1. Is there a correlation between epidemics of poliomyelitis and rain- 
fall? [See Am. J. P. H., Sept., 1917, p. 813.] 

2. Is there a higher correlation between flies and diarrhceal diseases 
among children than between diarrhceal diseases and other factors? 
[See Am. J. P. H., Feb., 1916, p. 143, also Mar., 1914, p. 184.] 

3. Is there a correlation between pneumonia and influenza? Is 
there a causal relation? [See Am. J. P. H., Apr., 1916, p. 316.] 

4. Is there a correlation between tuberculosis and housing? [See 
Am. A. J. P. H., Jan. 1913, p. 24.] 

5. Look up Dr. Fulton's extravaganza on the subject of statistical 
logic as applied to the problem of prostitution. [See Am. J. P. H., 
July, 1913, p. 661.] 

6. Study the correlation between plague and fleas. [Am. J. P. H., 
Aug., 1918, p. 572.] Is there strong presumptive evidence that in- 
fantile paralysis is spread by fleas? 

7. Express Mill's three canons of logic in your own words. 

8. Give examples of each in the field of epidemiology. 

9. What is meant by quantitative induction? What part do statis- 
tics play in this? [See Jevon's Lessons in Logic, Chap. XXIX.] 



CHAPTER XIV 
LIFE TABLES 

To the popular mind there is something mysterious and 
awesome about a hfe table. The insurance agent, wishing 
to sell you a policy, asks your age, consults a printed table 
and tells your " expectation of life " as so many years. What 
does this mean and how does he arrive at this expectation of 
life ? It does not mean that you will live so many years and 
then die. It means that it has been found in the past that 
most men who have attained your age have lived so many 
years after reaching that age. It cannot apply to everyone. 
You may live to be a hundred years old or you may die 
to-morrow. The future is uncertain for every individual. 
But the probability of your future longevity can be deter- 
mined by making a statistical study of a large group of people 
who have attained your age, to find out the average number 
of years which they lived after reaching that age. Instead 
of using the average, i.e., the mean we might find the median 
number of years lived, or even the mode. All three methods 
have been suggested, but that based on the mean is the one 
commonly used. Thus we see that there is nothing mysteri-< 
ous about the "expectation of life"; it has no divine origin. 
It is merely the application of the ordinary methods of 
statistics to the experience of mankind in living beyond a 
given age. 

Probability of living a year. — Although the expectation 
of life is used by insurance agents to impress the prospective 
purchaser with the fleeting character of human life, the rates 

422 



PROBABILITY OF LIVING A YEAR 423 

of insurance are not based directly on this expectation, but 
on the probabiHty of a person of given age Hving to be one 
year older. It is this chance of living from year to year, 
coupled with the growth of money at compound interest 
which determines what premium the insured at any age must 
pay. These actuarial methods are too complicated to be 
entered into here. In the very early days life insurance was 
virtually a lottery; now it is based on experience. If, as a 
result of better living conditions, the longevity of the insured 
is greater than the experience upon which the rates were 
based, the insurance company is the gainer because the 
premiums are continued for a longer time and the final pay- 
ment of the policy is postponed. If the company is a so- 
called mutual company, the benefit of increased longevity 
of the insured is distributed among the policy holders in the 
form of rebates. But should the longevity of the insured 
prove to be less than the experience upon which the rates 
were based the opposite condition would prevail. 

What is the chance of a person living from year to year? 
Obviously it is one minus the chance of dying. The chance 
of dying within one year at any age is nothing else than our 
old friend the specific death-rate for the given age. Thus if 
at age 20 the specific death-rate is 7.80 per 1000, the chance 
of dying within the year is 780 in 100,000, 0.0078 in 1, or 1 
chance in 128; at age 50 the chance is 0.01378, or 1 in 73; 
at age 70 it is 0.06199 or 1 in 16; at age 80 it is 0.14447, or 
1 in 7; at age 90, it is 0.45454, or 1 in 2.2. 

The chance of Hving through the year is 1 less the chance 
of dying. At age 20 the chance of living through the 
year is 99,220 in 100,000, i.e., 0.9920; at age 50 it is 0.98622; 
at age 70, 0.93801 ; at age 80 it is 0.85553; at 90 it is 0.54546. 
Or, to put it in another form, — at age 20 the chance of living 
a year is 99.2 in a hundred; at age 50, 98.6; at age 70, 93.8; 
at age 80, 85.5; at age 90, 54.5 in a hundred. 



424 



LIFE TABLES 



Thus a column showing for each age of life the probability 
of living a year can be made by subtracting the yearly 
specific death-rates from unity, and expressing the results 
in decimal parts of L We might call these specific life-rates, 
as they are the converse of the specific death-rates. 

This specific life-rate is never used in ordinary discussion, 
and there is little reason for using it, as it is probably better 
to think in terms of specific death-rates. It is the deaths 
which we are always trying to postpone. A table of specific 
death-rates and specific life-rates would look like this. 



TABLE 143 
SPECIFIC DEATH-RATES AND SPECIFIC LIFE-RATES 
(Abridged from the American Experience Mortality Table.) 





Population alive at 


Specific death-rate per 


Specific life-rate per 100,000 


Age. 


100,000 (number dying 


(number living through 






annually) . 


the year). 


(1) 


(2) 


(3) 


(4) 


10 


100,000 


749 


99,251 


20 


100,000 


780 


^9,220 


30 


100,000 


843 


99,157 


40 


100,000 


979 


99,021 


50 


100,000 


1,378 


98,622 


60 


100,000 


2,669 


97,331 


70 


100,000 


6,199 


93,801 


80 


100,000 


14,447 


85,553 


90 


100,000 


45,454 


54,546 



One reason why specific death-rates are not used more 
commonly is because people do not clearly understand them. 
The base, i.e., 100,000 persons, remains constant for all ages. 
Actually the number of persons alive is constantly decreasing 
as age advances. One says ''you start with 100,000 persons 
at age 10 and kill off 749 in one year, but the next year you 
have 100,000 again. I don't understand it." 



MORTALITY TABLES 



425 



Now life tables are definitely related to specific death-rates 
and they take into account this decreasing population. 

Mortality tables. — In order to make a life table we may 
first select some large class of people and determine the 
specific death-rates for each year of age. We start with a 
certain number of people ahve at a certain age. The in- 
surance companies commonly use age 10 because most 
insured persons are older than that, but we might use any 
other age. We might use age 0, and in making a life table 
for a general population this would be done. As an illustra- 
tion, however, let us take the American Experience Mortality 
Table, which starts at age 10 and which is limited to males. 
Another reason for taking age 10 is that it is a round number 
not far from the age at which the specific death-rate is the 
lowest. 

For convenience we start with 100,000 as a round number 
of persons alive at age 10. This number is called the radix 
of the computation. MVe might use a million or a thousand, 
but the former is hardly warranted by the precision of our 
specific death-rates, while the latter gives too many decimals. 

In the table, column (1) gives the age, and column (5) the 
corresponding specific death-rates obtained from the original 
data. In column (2) we start with 100,000 persons alive at 
age 10, of these 



92,637 In 


^ed to age 


20 


85,441 ' 


( 11 


30 


78,106 ' 


I (I 


40 


69,804 ' 


i a 


50 


57,917 ' 


i (■' 


60 


38,569 ' 


( ' It 


70 


14,474 ' 


( u 


80 


847 ' 


i u 


90 


' 


I a 


96 



These figures wfere obtained as follows: — 100,000 were 
alive at the beginning of age 10 and 740 per 100,000 died 



426 



LIFE TABLES 



TABLE 144 





AMERICAN EXPERIENCE MORTALITY 


TABLE 




Age. 


Num- 
ber 
living. 


Num- 
ber 
dying. 


No. of 
years 
expect- 
ation of 
life. 


No. dy- 
ing of 
each 
100,000 
annually. 


Age. 


Num- 
ber 
living. 


Num- 
ber 
dying. 


No. of 
years 
expect- 
ation of 
life. 


No. dy- 
ing of 
each 
100,000 
annually. 


(1) 


(2) 


(3) 


(4) 


(5) 


(1) 


(2) 


(3) 


(4) 


(5) 


10 


100,000 


749 


48.72 


749 


53 


66,797 


1,091 


18.79 


1,633 


11 


99,251 


746 


48.08 


752 


54 


65,706 


1,143 


18.09 


1,740 


12 


98,505 


743 


47.45 


754 


55 


64,563 


1,199 


17.40 


1,857 


13 


97,762 


740 


46.80 


757 


56 


63,364 


1,260 


16.72 


1,988 


14 


97,022 


737 


46.16 


760 


57 


62,104 


1,325 


16.05 


2,133 


15 


96,285 


735 


45.50 


763 


58 


60,779 


1,394 


15.39 


2,294. 


16 


95,550 


732 


44.85 


766 


59 


59,385 


1,468 


14.74 


2,472 


17 


94,818 


729 


44.19 


769 


60 


57,917 


1,546 


14.10 


2,669 


18 


94,089 


727 


43.53 


773 


61 


56,371 


1,628 


13.47 


2,888 


19 


93,362 


725 


42.87 


776 


62 


54,743 


1,713 


12.86 


3,129 


20 


92,637 


723 


42.20 


780 


63 


53,030 


1,800 


12.26 


3,394 


21 


91,914 


722 


41.53 


785 


64 


51,230 


1,889 


11.67 


3,687 


22 


91,192 


721 


40.85 


791 


65 


49,341 


1,980 


11.10 


4,013 


23 


90,471 


720 


40.17 


796 


66 


47,361 


2,070 


10.54 


4,371 


24 


89,751 


719 


39.49 


801 


67 


45,29.1 


2,158 


10.00 


4,765 


25 


89,032 


718 


38.81 


806 


68 


43,133 


2,243 


9.47 


5,200 


26 


88,314 


718 


38.12 


813 


69 


40,890 


2,321 


8.97 


5,676 


27 


87,596 


718 


37.43 


820 


70 


38,569 


2,391 


8.48 


6,199 


28 


86,878 


718 


36.73 


826 


71 


36,178 


2,448 


8.00 


6,766 


29 


86,160 


719 


36.03 


834 


72 


33,730 


2,487 


7.55 


7,373 


30 


85,441 


720 


35.33 


843 


73 


31,243 


2,505 


7.11 


8,018 


31 


84,721 


721 


34.63 


851 


74 


28,738 


2,501 


6.68 


8,703 


32 


84,000 


723 


33.92 


861 


75 


26,237 


2,476 


6.27 


9,437 


33 


83,277 


726 


33.21 


872 


76 


23,761 


2,431 


5.88 


10,231 


34 


82,551 


729 


32.50 


883 - 


77 


21,330 


2,369 


5.49 


11,106 


35 


81,822 


732 


31.78 


895 


• 78 


18,961 


2,291 


5.11 


12,083 


36 


81,090 


737 


31.07 


909 


79 


16.670 


2,196 


4.74 


13,173 


37 


80,353 


742 


30.35 


923 


80 


14,474 


2,091 


4.39 


14,447 


38 


79,611 


749 


29.62 


941 


81 


12,383 


1,964 


4.05 


15,860 


39 


78,862 


756 


28.90 


959 


82 


10,419 


1,816 


3.71 


17,430 


40 


78,106 


765 


28.18 


979 


83 


8,603 


1,648 


3.39 


19,156 


41 


77,341 


774 


27.45 


1,001 


84 


6,955 


1,470 


3.08 


21,136 


42 


76,567 


785 


26.72 


1,025 


85 


5,485 


1,292 


2.77 


23,555 


43 


75,782 


797 


26.00 


1,052 


86 


4,193 


1,114 


2.47 


26,568 


44 


74,985 


812 


25.27 


1,083 


87 


3,079 


933 


2.18 


30,302 


45 


74,173 


828 


24.54 


1,116 


88 


2,146 


744 


1.91 


34,669 


46 


73,345, 


848 


23.81 


1,156 


89 


1,402 


555 


1.66 


39,586 


47 


72,497 


870 


23.08 


1,200 


90 


847 


385 


1.42 


45,454 


48 


71,627 


896 


22.36 


1,251 


91 


462 


246 


1.19 


53,247 


49 


70,731 


927 


21.63 


1,311 


92 


216 


137 


0.98 


63,426 


50 


69,804 


962 


20.91 


1,378 


93 


79 


58 


0.80 


73,418 


51 


68,842 


1,001 


20.20 


1,454 


94 


21 


18 


0.64 


85,714 


52 


67,841 


1,044 


•19.49 


1,539 


95 


3 


3 


0.50 


100,000 



THE "VIE PROBABLE" 427 

during the year. Consequently, the number aUve at age 11 

was 100,000 - 749 = 99,251. In the next year the specific 

death-rate was 752 per 100,000. The number dying was, 

752 
therefore, 99,251 X ^ ^ = 746, and the number ahve at 

age 12 was 99,251 - 746 = 98,505. And so on. The num- 
ber dying each year is given in column (3) , the number living 
in column (2). At age 96 all were dead. 

These are the facts of the case, now how shall we use them ? 
There are three ways, which correspond to the mode, the 
median and the mean, and they are called respectively the 
''most probable life-time," the ''Vie Probable," and the 
"Expectation of Life." 

[^ The *' most probable life-time." — The figures in column 3 
form a frequency curve, the mode of which is 2505. There 
are more deaths at age 73 (i.e., age 73-74) than at any other 
age. 73 is the fashionable, modish age to die. The chance 
of dying at that age is greater than at any other age. 

The difference between a given age and 73 years is called 
"the most probable hfe-time." At age 10, it is 73 — 10 = 
63; at age 20 it is 53; and so on. Above the age 73 the 
"most probable life-time" becomes a negative quantity, and 
this is the objection to the use of this computation. It is 
applicable only to the first part of the frequency curve. 

The **Vie Probable." — The "Vie Probable" is the 
number of years which a person (at a stated age) has an even 
chance of living. It is the difference between a given age 
and the age at which the number of persons alive is one-half 
the number alive at the given age. The latter is the median 
age to which the persons who passed the given age lived. 

At age 10 there are 100,000 persons alive. One-half of 
this number, i.e., 50,000, are alive at age 64.5 =b. Hence 
64.5 — 10 = 54.5 is the "vie probable." In this period of 
time the chance of living or dying is just even. 



428 LIFE TABLES 

At age 20, there are 92,637 persons alive. One-half of this 
number, i.e., 46,318, were still alive at age 66.5. Hence the 
^'vie probable," for age 20 is 66.5 — 20 = 46.5 years. 

The *' Expectation of Life." — The ''Expectation of 
life" naeans the average number of years that persons of a 
given age will probably survive. It is obtained by finding 
the average of the lengths of life of all the persons who lived 
beyond the given age. 

Thus of the 100,000 alive at age 10, 3 lived to the age of 95, 
that is, they lived for (95 — 10 = ) 85 years after the age of 
10. 21 lived to age 94, i.e., 84 yea'rs. But these 21 include 
the 3 who lived to age 95, so there were 18 who lived 84 
years. 79 lived 83 years, but these include both the 3 and 
the 18, so in addition to them (79 — 21 =) 58 lived 82 years. 
And so on. The weighted averages of all of these lives gives 
what is called the expectation of life. These results are 
given in column (4) . 

In obtaining the figures for column (4) it is most con- 
venient to begin at the higher ages and work backward. 

At the beginning of age 95, there were 3 persons alive; at 

the end there were none alive. Not knowing at what part 

of the year they died the best assumption is that they died 

(on an average) at the middle of the year, i.e., they lived 

one-half year. Hence at age 95, the average length of the 

3 X - 
lives was — 5-^ =0.50 year. This is the expectation of life 

o 

at age 95. 

At age 94, 21 persons were alive. 3 of these lived IJ years 
each; the other 18 died within the year, and may be said to 
have lived one-half year. Hence we have : 

3 X 1.5 = 4.5 
18 X 0.5 = 9.0 
21 13.5 and 13.5 ^21 =0.64 yr. 

Hence at age 94 the expectation of life is 0.64 year. 



COMPARISON OF THE THREE RESULTS 



429 



At age 93 we have : 

3 X 2.5 = 7.5 
18 X 1.5 = 27.0 
58 X 0.5 = 29^ 
79 63.5, and 63.5 X 79 = 0.80 year. 

In this way we find that at age 10, the average number of 
years Hved by those who passed age 10, was 48.72 years. 
At age 20 it was 42.20 years; at age 30 it was 35.33 years, etc. 

Comparison of the three results. — The U. S. Life Tables 
for 1910 give the '^complete expectation of hfe" (computed 
on the basis of the mean), and from the tables may be ob- 
tained the ''most probable life-time"" (based on the mode) 
and the ''vie probable" (based on the median). The follow- 
ing figures give the results for age zero, that is, they show 
the expectation of life at birth. 

TABLE 145 

COMPARISON OF "EXPECTATION OF LIFE," "VIE PROB- 
ABLE" AND "MOST PROBABLE LIFE-TIME" 



Original registration states. 



(1) 



White males 

White females 

Negro males 

Negro females 

White males in cities 

White males in rural part . . 

White females in cities 

Wliite females in rural part 

Males in Massachusetts . . . . 
Females in Massachusetts. . 



Expecta- 
tion of life. 
(Mean.) 


" Vie prob- 
able." 1 
(Median.) 


(2) 


(3) 


50.23 
53.62 
34.05 
37.67 

47.32 
55.06 
51.39 
57.35 

49.33 
53.06 


59.30 
63.27 
34.85 
40.58 

55.00 
65.33 
60.73 
67.38 

58.82 
62.74 



Most prob- 
able 1 life- 
time. 
(Mode.) 



(4) 



74.0 
73.5 
59.5 
65.5 

68.5 
76.5 
71.5 
76.5 

69.5 
74.5 



Approximate. 



430 LIFE TABLES 

Life tables based on living population. — Life tables are 
usually computed in another way. They are based on the 
population living at each age as shown by the census returns 
or by data collected by the insurance companies. Thus we 
may assume that the figures in column (2) have been ob- 
tained in this way. If we start with 100,000 persons alive 
at age 10 and find that 99,251 were alive at age 11 then the 
number of deaths during the year must have been 100,000 — 
99,251, or 749. Between ages 11 and 12 the deaths were 
99,251 — 98,505, or 746; and so on. By this method we 
compute the deaths, and we may also compute the specific 
death-rates for each age. This method justifies the use of 
the term life tables, as the results are based on the living and 
not on the dying. It is obvious that migrations of population 
interfere somewhat with this method. It is obvious, also, 
that concentrations of population on the round numbers 
present another difficulty. As a matter of practice the 
ragged data must be smoothed out before a life table can be 
constructed; otherwise the computed expectations of life 
would themselves be erratic. These errors of round numbers 
creep into the computations of specific death-rates, so that 
in any case it is necessary to do a certain amount of '^ smooth- 
ing" before computing life tables. One method coromonly 
used is that known as '^osculatory interpolation," which 
may be found described in such books as Vital Statistics Ex- 
plained, by Burn. 

Still another method of computing a life table is to base it 
wholly on the distribution of deaths, making use of certain* 
mathematical formulas for frequency curves.^ 

Mathematical formula for computing the expectation of 
life. — There is a mathematical formula for the computa- 
tion of the expectation of life by the use of which the labor 
may be shortened. It is usually stated as follows: 

^ Arne Fisher. Note on the Construction of Mortality Tables by 
means of Compound Frequency Curves. Proc. Casualty Actuarial and 
Statistical Society of America, Vol. IV, Ft. 1, No. 9. 



EARLY HISTORY OF LIFE TABLES 431 

® ilx+ 'kx+D + ^(x+2) + kx+Z) + • • • 1 _L n 

e.= j-^ —=2 + ^- 

n — ^(^+1)"^ kx+2) + kx+3) + • • • 

^x 
o 

e, = expectation of life, in years, at age x, 

Ix = number of persons living at age x. 
kx+i) = number of persons living at age x -{- 1. 
kx+z) = number of persons living at age x + 2, etc. 

For a more detailed description of these methods the 
reader is referred to such books as United States Life Tables, 
1910, Bureau of the Census, prepared by Prof. James W. 
Glover and published in 1916; Life Assurance Primer, by 
Henry Moir; Vital Statistics, by Newsholme; Mortality 
Laws and Statistics, by Robert Henderson. 

Early history of life tables. — It is not surprising that 
most of the life tables which have been computed have been 
confined to males of insurable age. Halley, the British 
astronomer, famous for the comet which bears his name, was 
the first to use the method. This was in 1692 and related 
to the town of Breslau. Other famous tables are the North- 
ampton Table of 1762, the Carlisle Table of 1815 and Dr. 
Farr's English Table of 1851. 

In 1843 seventeen American insurance companies com- 
bined their experiences and published a table known as the 
Actuaries or Combined Experience Table. It was based on 
84,000 policies. The American Experience Table of Mor- 
tality, now recognized by the insurance companies as the 
standard for America, was formed by Sheppard Homans in 
1868. It is supposed to have been based on the experience of 
the Mutual Life Insurance Company of New York. 

In 1869 the H^ Table was published in England. H^ 
means Healthy Males. It was based on 180,000 policies. 
Then there is an 0^ Table (ordinary life, males) based on 
over 400,000 lives. This is the Canadian standard. 



432 



LIFE TABLES 



Recent life tables. — In 1898 Dr. Samuel W. Abbott 
published in the annual report of the Massachusetts State 
Board of Health for that year/ a life table for Massachusetts. 
This is one of our best American papers on the subject. 

Dr. Guilfoy, the statistician of the New York City Board 
of Health, has published the following interesting comparison 
between the expectations of life in 1879-81 and 1909-11. 
The changes which have taken place during the interval are 
striking. The figures are as follows: 

TABLE 146 

APPROXIMATE LIFE TABLES FOR THE CITY OF NEW 

YORK BASED ON MORTALITY RETURNS FOR THE 

TRIENNIA 1879-1881 AND 1909-1911 





Expectation of life, 


Expectation of life. 


Gain {+) or loss (— ) in 


Years oi 
mor- 


1879 to 1881. 


1909 to 1911. 


years of expectancy. 


tality, 
ases. 


Males. 


Fe- 
males. 


Per- 
sons. 


Males. 


Fe- 
males. 


Per- 
sons. 


Males. 


Fe- 
males. 


Per- 
sons. 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7)' 


(8) 


(9) 


(10) 


-5 


39.7 


42.8 


41.3 


50.1 


53.8 


51.9 


+ 10.4 


+ 11.0 


+10.6 


5 


44.9 


47.7 


46.3 


49.4 


52.9 


51.1 


+ 4.5 


+ 5.2 


+ 4.8 


10 


42.4 


45.3 


43.8 


45.2 


48.7 


46.9 


+ 2.8 


+ 3.4 


+ 3.1 


15 


38.2 


41.2 


39.7 


40.8 


44.2 


42.5 


+ 2.6 


+ 3.0 


+ 2.8 


20 


34.4 


37.3 


35.8 


36.6 


40.0 


38.3 


+ 2.2 


+ 2.7 


+ 2.5 


25 


31.2 


34.0 


32.6 


32.7 


36.0 


34.3 


+ 1.5 


+ 2.0 


+ 1.7 


30 


28.2 


31.0 


29.6 


28.9 


32.1 


30.5 


+ 0.7 


+ 1.1 


+ 0.9 


35 


25.3 


28.1 


26.7 


25.4 


28.4 


26.9 


+ 0.1 


+ 0.3 


+ 0.2 


40 


22.5 


25.2 


23.9 


22.1 


24.7 


23.4 


- 0.4 


+ 0.5 


- 0.5 


45 


19.8 


22.4 


21.1 


18.9 


21.1 


20.0 


- 0.9 


- 1.1 


- 1.1 


50 


17.2 


19.4 


18.3 


15.9 


17.7 


16.8 


- 1.3 


- 1.7 


- 1.5 


55 


14.5 


16.4 


15.4 


13.2 


14.6 


13.9 


- 1.3 


- 1.8 


- 1.5 


60 


12.2 


13.8 


13.0 


10.8 


11.8 


11.3 


- 1.4 


- 2.0 


- 1.7 


65 


9.9 


11.2 


10.5 


8.8 


9.4 


9.1 


- 1.1 


- 1.8 


- 1.4 


70 


8.5 


9.3 


8.9 


6.9 


7.5 


7.2 


- 1.6 


- 1.8 


- 1.7 


75 


7.1 


7.5 


7.3 


5.3 


5.7 


5.5 


- 1.8 


- 1.8 


- 1.8 


80 


6.2 


6.5 


6.4 


4.1 


4.5 


4.3 


- 2.1 


- 2.0 


- 2.1 


85+ 


5.4 


5.5 


5.5 


2.0 


2.4 


2.2 


- 3.4 


- 3.1 


- 3.3 














+24.8 


+28.7 


+26.6 




Balan 


ce . . . . 










-15.3 
+ 9.5 


-17.6 
+ 11.1 


-16.6 




• 










+ 10.0 



See State Sanitation, Vol. II, p. 300, by G. C. Whipple. 



A FEW COMPARISONS 433 

United States life tables. — In 1916 the Bureau of the 
Census pubhshed a special report entitled United States 
Life Tables, 1910, prepared under the direction of Prof. 
James W. Glover of the University of Michigan. This was 
the first report of its kind in America. The tables are based 
on the general unselected population, and, therefore, differ 
from the life tables of the insurance companies. The radix 
is 100,000 at age 0. The data were obtained from the U. S. 
Census of 1910. Expectations of life are computed by- 
months up to one year of age, and after that by years up to 
age 106. Separate tables are given for males, for females 
and for botfh sexes combined; there are separate tables also 
for negroes and whites, and for native and foreign born 
whites; for cities and for rural districts, — all of these re- 
lating to the population of the original registration states,- 
namely, the New England states. New York, New Jersey, 
Indiana, Michigan and the District of Columbia. Separate 
tables for males and for females are given for the states of 
Indiana, Massachusetts, Michigan, New Jersey and New 
York. 

These tables are well prepared and their results are of much 
interest. Besides giving the expectations of life computed 
in the usual way, computations are made on the assumption 
of a stationary population, that is one where the general 
death-rate is equal to the general birth-rate. These have 
the advantage of excluding the effect of emigration results 
and immigration, and from them one can compare the death- 
rates of different communities for the population above a 
given age. For these results the reader is referred to the 
original report. 

A few comparisons. — It will be interesting to make a 
few comparisons of the expectations of life at certain ages for 
different classes of people and at different ages. For greater 
details the reader should consult Professor Glover's report. 



434 



LIFE TABLES 



TABLE 147 
EXPECTATIONS OF LIFE, 1910 



Age. 
Original registration states. 



(1) 



Native white males 

Native white females 

Foreign-born white males.. . 
Foreign-born white females . 

Negro males 

Negro females 

White males in cities 

White males in rural part. . . 

White females in cities 

White females in rural part . 

'Males in Indiana 

Males in Michigan 

Males in Massachusetts .... 

Males in New Jersey 

Males in New York 



(2) 



50.58 
54.19 



34.05 
37.67 

47.32 
55.06 
51.39 
57.35 

54.70 
53.86 
49.33 
49.08 
47.89 



10 



(3) 



51.93 
54.43 
50.30 
52.24 
40.65 
42.84 

49.13 
54.53 
52.22 
55.54 

53.91 
54.09 
51.14 
50.31 
49.40 



20 



(4) 



43, 

45 

41 

43, 

33. 

36, 



40.51 
45.92 
43.51 
46.86 

45.44 
45.57 
42.48 
41.66 
40.79 



30 



(5) 



35.61 
37.98 
33.71 
35.31 
27.33 
29.61 

32.61 
38.10 
35.52 
39.05 

37.76 
37.76 
34.55 
33.86 
33.01 



40 



(6). 



28.33 
30.33 
26.03 
27.55 
21.57 
23.34 

25.32 
30.20 

27.88 
31.15 

29.99 
29.81 
26.97 
26.57 
25.88 



50 



(7) 



21.20 
22.78 
19.08 
20.09 
16.21 
17.65 

18.59 
22.43 
20.53 
23.27 

22.38 
22.10 
19.79 
19.67 
19.28 



70 



(8) 



9.09 
9.80 
8.40 
8.67 
8.00 
9.22 

8.14 
9.36 
8.99 
9.76 

9.29 
9.17 

8.58 
8.65 
8.58 



The greater longevity of females as compared with males 
is evident throughout the tables. It is greater for native 
whites than for foreign born whites, greater for whites than 
for negroes, greater for rural districts than for cities. The 
differences between the states depend upon differences in the 
composition of the population, and upon urban and rural 
conditions. 

It is interesting also to compare the specific death-rates for 
the corresponding ages. The relations between these and 
the expectations of life are in a general way reciprocal. The 
specific death-rates are lower in the rural districts than in 
the cities, especially in the early and the later years; in middle 
life there is less difference. The differences between whites 
and negroes are very striking. 



EXERCISES AND QUESTIONS 



435 



TABLE 148 
SPECIFIC DEATH-RATES 



Age. 
Registration area. 





10 

(3) 


20 


30 


40 


50 


70 


(1) 


(2) 


(4) 


(5) 


(6) 


(7) 


(8) 


Native white males 

Native white females 

Foreign-born white males.. . 


126.02 
104.60 


2.37 
2.06 
2.47 
2.09 
5.02 
5.18 

2.59 
2.07 
2.23 
1.80 


4.82 
4.40 
5.10 
3.65 
11.96 
10.74 

4.93 
4.83 
4.10 
4.41 


7.14 
6.13 
5.80 
5.84 
14.96 
12.02 

7.22 
5.39 
6.33 
5.46 


10.02 
7.76 

10.53 
8.55 

21.03 

17.50 

12.10 
7.06 

8.83 
6.65 


21.20 
11.68 
17.92 
14.42 
31.42 
25.52 

19.17 

10.65 

14.44 

9.91 


57.20 
50.24 
70 79 


Foreign-born white females. 




67.87 


Negro males 


219.35 
185.07 

133.80 
103.26 
111.23 

84.97 


83.98 


Negro females 


71.27 


White males in cities 

White males in rural part. . . 

White females in cities 

White females in rural part . 


74.20 
52.93 
63.50 
49.92 



EXERCISES AND QUESTIONS 

1. Compare the life table for New Haven with that for the U. S. 
Registration Area. [See Am. J. P. H., Aug., 1918, p. 580.] 

2. Compute a life table for some city, to be assigned by the in- 
structor. 

3. Find your own "probability of living a year," "vie probable," 
*'most probable life-time," and "expectation of Hfe." 



CHAPTER XV 

A COMMENCEMENT CHAPTER 

This last chapter is to be something Hke the day after col- 
lege commencement. On the day before the student regards 
his work as finished; his exercises are all completed, he has 
passed his examinations, he is to be graduated. But on the 
day after commencement he finds himself plunging into a 
world of problems yet unsolved; he sees that most of the 
things he is called upon to do were not in his curriculum; 
that he must learn to do these things for himself. Little by 
little he comes to realize that what his stupid old profes- 
sors had been trying to do was not to tell him all there was 
to know in the world but to teach him how to think 
and how to use tools. He had heard much of principles, 
and laws and formulae and synopses and all that, and had 
regarded them as the dry parts of his courses — the neces- 
sary evils. But little by little he finds that these g'eneral 
principles, these almost self-evident ideas, help him to solve 
his problems; that his systematic methods of going at a 
thing help him to do his work more easily and quickly; 
that by following the dry old laws of logic, his conclusions 
are somehow better than those of the other fellow who does 
not take the trouble to see that all the steps in the prob- 
lem are " necessary and sufficient." In short, he comes to 
realize that his education has enabl'^d him to do his work 
easier and better and has given him intellectual confidence. 
If it doesn't do this for him he has wasted his opportunities 
in college. 

436 



MILITARY STATISTICS 437 

In the preceding chapters of this book the author has en- 
deavored to place the emphasis not on the subject matter 
but on methods of procedure, to outhne the simpler prin- 
ciples of the statistical method as applied to studies in 
demography, to warn against. the common fallacies which 
so often creep into discussions of vital statistics, and to urge 
students and health officers not to be content with such 
things as general rates but to seek the answers to their prob- 
lems by methods of statistical analysis and the use of specific 
rates and ratios. 

Let us now take an outlook upon some of the problems 
of demography as they come piling in upon the health officer 
from day to day. And if, for convenience' sake, we take 
them at random, one after the other, without order or system 
we shall simulate more nearly e very-day practice. If we 
can solve this and that problem or if we can see the steps 
in the solution we shall know that we have acquired the 
use of the tools of the statistician, and will have confidence 
in our own studies. This chapter will also include certain 
subjects which have not logically found a place in the pre- 
ceding chapters. Several of these subjects might easily be 
expanded into chapters of their own. 

Military statistics. — In general the vital statistics of 
armies are computed in the same way as those of civil pop- 
ulations, but instead of using the mid-year estimated 
population, the mean strength for the year is used as a 
basis of rates. An army does not increase in numbers as a 
population grows, slowly by geometrical progression, but 
is kept up to a fairly constant strength or is suddenly 
increased or decreased according to demands made upon it. 
An army represents a selected population, — males be- 
tween certain age limits, and above set standards of health 
and physique. Rates computed for armies are therefore 
specific rates and they must not be compared with general 



438 A COMMENCEMENT CHAPTER 

rates. The health of the soldiers is carefully looked after 
by the surgeons, who are obliged to keep records; hence 
the morbidity records are more complete than in the case 
of the civil population. 

Since 1894, when an international commission for the uni- 
fication of medical statistics met at Budapest, tables of 
statistics made up according to certain schedules have been 
published for most armies. These may be found in the 
annual reports of the Surgeon General of the U. S. A. In 
the report for 1916 we find that in the entire U. S. army 
of 93,262 enlisted men in 1915 the sick admissions " to quar- 
ters " and " to hospitals " amounted to 745 per 1000. 
This does not mean 745 different men, for sometimes the 
same man was admitted more than once. Of these 96 per 
cent returned to duty, i.e. recovered, 0.65 per cent died, 
and 3.4 per cent were '^ otherwise disposed of." The 
death-rate for the mean strength was 4.6 per 1000. The 
annual number of days lost through sickness was 9.44 for 
each soldier, or 12.7 for each " admission." In the pub- 
lished tables the figures are classified according to the 
location of the troups, the arms of the service, the season, 
the larger garrisons, and according to the cause of the sick- 
ness or death. It should be observed that in the interna- 
tional tables for the army the international list of diseases, 
as given on page 257, is not followed. The Surgeon General 
of the United States uses it, however, in the body of his 
report. 

In 1915 in the entire U. S. army (103,842 officers and 
enlisted men) the following were the rates per 1000 of 
mean strength: 



MILITARY STATISTICS 



439 



TABLE 149 
VITAL STATISTICS OF U. S. ARMY: 1915 





Death-rates per 1000. 




From disease. 


From injury. 


Total. 


(1) 


(2) 


(3) 


(4) 


Admissions 

Discharged on certificate of 

disability 

Died 

Total losses 


597.0 

12.6 

2.5 

15.1 


129.2 

1.4 
1.9 
3.3 


726.2 

14.0 

4.4 

18.4 







The percentage of soldiers constantly non-effective was 
2.5 per cent. 

If we look back a few years we find that the health of 
the army has been improving. 



TABLE 150 

HOSPITAL ADMISSION RATES AND PERCENTAGE 
OF NON-EFFECTIVES, U. S. A. 



Year. 


Admission-rate 
per 1000 


Non-effectives, 
per cent. 


(1) 


(2) 


(3) 


1906 
1907 
1908 
1909 
1910 
1911 
1912 
1913 
1914 
1915 
1916 


1118 
1102 
1079 
964 
870 
858 
806 
666 
660 
726 
597 


4.8 
4.4 
4.2 
4.1 
3.5 
3.2 
2.9 
2.4 
2.4 
2.5 
2.5 



440 A COMMENCEMENT CHAPTER 

Army diseases. — In the consideration of army diseases 
one must distinguish between peace times and war times; 
one must also distinguish between the diseases which cause 
death and those which render the men non-effective. 

In 1915 the specific death-rates among the American 
enhsted men in the U. S. A. were, in order of their im- 
portance, as follows: 

Per 100,000 

Tuberculosis 33 

Pneumonia (lobar) 31 

Organic heart disease 23 

Measles 23 

Appendicitis 13 

Epidemic cerebro-spinal meningitis 11 

The principal causes of discharge were : 

Per 1000 

Mental alienation 3.30 

Tuberculosis • 1.79 

Flat foot 1.25 

Venereal disease 0.82 

Epilepsy 0.69 

Organic heart disease 0.50 

The admission and non-effective rates for white enlisted 
men were: 



ARMY DISEASES 



441 



TABLE 151 

ADMISSION RATES AND PERCENTAGE OF NON-EFFECTIVES 
FROM PARTICULAR DISEASES, U. S. A. 





Admission rate, 
per 1000 


Non-effectives, 
per cent. 


(1) 


(2) 


(3) 


Venereal diseases 


106 

3 

4 

35 

47 

9 

24 

10 

35 

32 

7 

6 

4 


47 


Tuberculosis 


0.17 


Mental alienation 


09 


' Bronchitis 


06 


Tonsilitis 


0.07 


Appendicitis 


0.06 


Malaria 


0.05 


Mumps 


0.05 


Influenza 


05 


Diarrhcea and enteritis 


04 


Measles 


0.05 


Articular rheumatism 


0.04 


Hernia 


0.04 







In war times we have to consider the venereal diseases, 
syphiUs, gonorrhoea, etc.; the diarrhoeal diseases, typhoid 
fever, cholera, dysentery; the insect-borne diseases, typhus 
fever, relapsing fever, trench fever, malaria, etc.; scurvy — 
besides all sorts of diseases associated with wounds. No 
attempt will be made here to discuss these war diseases, 
because the Great War will yield statistics better and 
more complete than any which we now have. Some day 
it will be in order to make comparisons between the 
Civil war, the Spanish war and the present Great War. 
We shall then see what enormous strides have been taken 
in sanitation, in the use of antitoxins, in providing proper 
food, in the enforcement of the rules of personal hygiene, 
in the treatment of the sick and wounded, in the- ambulance 
and hospital service, in the protection of the health of the 
civil population in war time in factory and home. One 



442 A COMMENCEMENT CHAPTER 

gratifying result of the war seems assured — ■ a world-wide 
up-lift in public health. We shall hereafter need world- 
wide vital statistics, that is, we shall need the science of 
demography. 

Effect of the Great War on demography. — A thousand 
and one questions have arisen as a result of the war. 

What are we to do with the enormous number of non- 
resident males in the United States? How are we to 
compute death-rates? Will our usual methods have to 
be modified as an emergency measure? 

What effect has the war had on the marriage-rates, 
birth-rates and death-rates? A big hole is sure to be made 
in the male population for the ages of youth and early 
manhood; fewer young men of twenty in 1920 will mean 
fewer men of thirty in 1930 and fewer men of forty in 
1940! How will this alter the general death-rate? Will 
the birth-rate rise as a natural reaction to war's • destruction 
or will hard economic conditions keep it low? Can we learn 
anything from past wars on this matter? 

Typhoid fever, the past scourge of armies, has been al- 
most completely conquered. Will the venereal diseases 
also be conquered? Will the Great War point out the way 
to this end? 

What has been the effect of reduced food rations on health 
and physique? Will the loss of the most vigorous young 
men lower the standards of physique by hereditary in- 
fluences? 

Will the lessons in hygiene and sanitation be so well learned 
that their benefits will offset other baneful influences? 

We knew approximately the standing of the nations 
before the war as to population, natural rates of growth, 
migrations, death-rates, and so on — how will these nations 
stand after the war? Who will be the greatest losers? 
What will be their most serious losses? 



STATISTICS OF INDUSTRIAL DISEASE 443 

Such questions as these force themselves upon us. Demog- 
raphy will be the science looked to for the answers. 

Hospital statistics. — There are many hospitals in the 
country and they are an increasingly important factor in 
the control of disease. Some of these hospitals keep good 
records of their cases and some publish them. Other hos- 
pitals keep very inadequate records and publish nothing. 
Uniformity in this matter is most desirable, as a good op- 
portunity for collecting facts in regard to certain non- 
reportable diseases and in regard to the fatality of these 
diseases is being lost. 

Several plans for unifying hospital statistics have been 
suggested. Dr. Charles F. Bolduan,^ of the New York 
City Health Department, suggested the idea of a dis- 
charge certificate, to be filled out for each case on leaving 
a hospital, — a certificate comparable to the ordinary death 
certificate. Another method is to have the annual re- 
ports (or monthly reports) made out on some fixed schedule 
of statistics and submitted to some central authority.^ 
Perhaps the U. S. Public Health Service may some day 
take the lead in the collection of the important data to be 
secured from hospitals. See also page 471. 

Statistics of industrial disease. — Statistical studies of 
industrial diseases are becoming increasingly numerous. 
It is a most complex and difficult branch of the subject. 
At the outset we are met with the fundamental difficulty of 
defining occupations. The extent of this difficulty may be 
appreciated from the fact that in 1915 the U. S. Bureau of the 
Census published an ^' Index to Occupations" which covered 
over four hundred pages and included 9000 occupational des- 
ignations. The report makes 215 main classes, 84 of which 
are subdivided. This list has been given in Chapter VIII. 

1 N. Y. Medical Journal, Mar. 29, 1913. 

2 Amer. Jour. Pub. Health, Apr., 1918, 



444 



A COMMENCEMENT CHAPTER 



A second difficulty is due to the migration of laborers 
from place to place, and from .one class to another. A 
third, which grows out of the other two, is the difficulty of 
getting constant, well-defined classes to serve as the basis 
of the computation of rates and ratios. A fourth is the 
oft repeated error of concealed classification. These and 
other minor difficulties have compelled us to resort to 
the use of specially gathered statistics, which are often not 
truly representative of the conditions discussed. 

For example, the Massachusetts General Hospital re- 
cently made a study of lead poisoning in its Industrial 
Clinic. During the first year of this clinic 148 cases of 
lead poisoning were diagnosed in the hospital as against 
147 during the previous five years. 

This was found by sifting out of the hospital admissions 
by a* trained worker those suspected of being exposed to 
special industrial hazard. A study of these 148 cases gave 
an industrial distribution as follows: 

TABLE 152 



Occupation. 



(1) 



Painters 

House 

Others 

Shipyard and navy yard . . . . 

Rubber workers 

Brass foundrymen 

Lead and lead oxide worker . 

Plumbers 

Printers 

Miscellaneous. 

Non-industrial 

Total 



Number 
exposed. 



(2) 



217 



54 

169 

9 



42 

64 

135 



Number 


Per cent 


cases. 


poisoned. 


(3) 


(4) 


68 


31 


56 




12 




16 


30 


■ 11 


7 


4 


44 


6 




8 


19 


11 


17 


14 


10 


10 




148 





ECONOMIC CONDITIONS AND HEALTH 445 

An attempt to ascertain the rate of attack was made by 
ascertaining as well as possible the number of persons 
exposed. These rates are, of course, far too high ; 31 per cent 
of all painters did not get lead poisoning, but only 3 1 per cent 
of the exposed persons who were sorted out in this indus- 
trial clinic. The report does not err in this respect but the 
reader may get a false impression unless he reads thought- 
fully. The underlying idea of this clinic is excellent and 
the work, unfortunately interrupted, was already yielding 
excellent results. -The danger of lead poisoning of men 
engaged in certain occupations in ship yards was clearly 
shown. 

Economic conditions and health. — Poverty and disease 
mutually influence each other. We cannot expect to 
solve the problem by attacking either alone. It is most 
difficult to separate cause from effect. In fact, there is a 
third major .factor which we may call ignorance — and 
all three are mutually dependent. Then there are many 
minor factors. 

We can correlate these things by statistics, and that is 
worth while because it calls attention to the problems; 
but the plan of attack must rest upon the fact that the 
different conditions are mutually related. If we help only 
a little to raise the economic and hygienic conditions 
the result is an accelerating social advance; to aid one 
without the other does not bring about permanent 
betterment. 

A glimpse at these mutual relations, as shown by 
Warren and Sydenstricker,^ is instructive. They classified 
the health of certain garment workers with respect to the 
annual earnings of the heads of families as follows: 

1 Pub. Health Reports, May 26, 1916, p. 1298. 



446 



A COMMENCEMENT CHAPTER 



TABLE 153 
HEALTH OF GARMENT WORKERS 





Annual earnings. 




$500 


$500-$699 


$700 


(1) 


(2) 


(3) 


(4) 


Number of persons 


381 

$382 
$19- 

38% 
$988 

5.36 

3.78 ■ 

2.99 

0.78 

206.9 

25.00 
85.94 

9.94 
5.64 


581 

$577 
$23 

48% 
$1196 

5.38 
3.34 

2.78 
0.56 

167.2 

15.02 
86.99 

5.65 
5.30 


462 


Ave. annual earnings 


$866 


Ave. rate of weekly earnings 


$27 


Per cent which actual earnings were of 
maximum possible earnings 


61% 


Maximum possible earnings for year . . . 

Ave. number of persons per family 

Ave. number of children born per family 
Ave. number of children living per 
family 


$1404 

4.88 
2.75 

2.43 


Ave. number of children dead per family 
Infant mortality rate. 


0.32 
116.5 


Per cent of male married garment 
workers who were poorly nourished. . 

Ave. haemoglobin index, Talquist 

Per cent with haemoglobin index under 
80 


12.72 
87.35 

4.42 


Per cent of family heads tuberculous. . . 


0.44 



Accidents and accident-rates. — Injuries and deaths 
from accidental causes are attracting much attention 
nowadays, and rightly so. The death-rate from accidents 
in the United States is far greater than from typhoid fever. 
Only a few years ago it was more than 100 per 100,000 of 
population. Some of the principal causes are railroad 
accidents, falls, drowning and burns, but there are many 
accidents associated with different industries. All of 
these present interesting problems for study and each 
should be studied by itself. 

Taking accidents as a general class, we find that the 



ACCIDENTS AND ACCIDENT-RATES 447 

specific death-rates follow closely the- death-rates from all 
causes, decreasing from the first year to a minimum be- 
tween ages 10-14 and then increasing steadily to the 
highest ages. Owing to the age distribution of population 
we find the mode of the accident distribution curve occur- 
ring somewhere in age group 25-29 years. 

In the case of railroad accidents among males the mode 
is found in age-group 25-29 years, that is, the largest 
number of accidents occurs among males at that period; 
in the case of falls the mode is in age-group 45-49; in the 
case of drowning it is at age 20-24. The specific death-rate 
from railroad accidents is low until the age of twenty, when 
it rises to above 30 per 100,000 and fluctuates between 30 
and 50 for all higher age-groups. -The specific death-rate 
from falls rises steadily from the tenth year and above 75 
years of age exceeds 100 per 100,000. The specific death- 
rate from drowning on the other hand is highest at about 
twenty years of age. Except for falls the accident-rates 
from the major causes are higher for males than for females. 

If time permitted it would be interesting to follow up this 
subject of accidents and find the seasonal distribution and 
classify them in other ways. 

In studying accidents in industrial establishments we 
must ask the usual questions, — where, when, what, how, 
who, and answer them by collecting the necessary statistics. 
It does not do to follow popular impressions in these mat- 
ters. Thus it is sometimes said that most accidents occur 
" at the end of a tired day," yet statistics collected in Massa- 
chusetts by the Industrial Accident Board showed that it is 
between 9 and 10 a.m. and 2 and 3 p.m. that accidents are 
most frequent. Yet this general statement is not enough. 
We need to know what kinds of accidents are meant. Per- 
haps some kinds of accidents do occur at the end of the 
working day. Then there are daily differences to be con- 



448 A COMMENCEMENT CHAPTER 

sidered, and seasonal differences, as well as differences due 
to the weather. In the case of the English munition fac- 
tories, which run night and day, the accident mode occurs 
in the evening. One runs a great risk in generalizing from 
composite statistics. 

There are various ways of expressing accident rates. 
One is the ratio between annual accidents and number of 
employees. Another is between annual accidents and the 
number of full time workers, i.e., 300 days per year. 
Another is between days lost through accident and full 
time workers. Differences in the severity of the accidents 
are also important from an economic point of view. 

Age distribution of cases of poliomyelitis. — One of the 
diseases which has recently attracted attention is Anterior 
Poliomyelitis, commonly known as infantile paralysis. 
Many attempts have been made to correlate the occur- 
rences of this disease with factors which might point to 
the manner of its communic ability. There is an excellent 
opportunity here for original statistical work based on re- 
cently accumulated data. As bearing on the theory of 
contact as a major element in its communicability the 
age distribution of the cases is important. The disease is 
essentially one of the early ages. A recent study by the 
author appears to indicate that the median age is inversely 
proportional to the density of population. This is like- 
wise true for measles, whooping cough and similar diseases. 

It has been noticed that if the cases of poliomyelitis are 
plotted on logarithmic probability paper they tend to fall 
on a straight line, except that above the upper decent ile 
there is an irregular divergence from the straight line. 
From this diagram it is easy to read off the median age 
or the per cent of cases below any age or between given 
ages. Fig. 63 shows that in the populous city of New 
York the median age was 2.5 years, in Boston 3.7 years, 



AGE DISTRIBUTION OF CASES OF POLIOMYELITIS 449 



-•05300 1^ O 




O C3 OO t>. Q 



450 A COMMENCEMENT CHAPTER 

and in Minnesota 4.6 years. Similar differences, were 
observed in the upper decentiles. These data are not 
strictly comparable as they were not for the same year and 
are presented merely to show the advantage of this method 
of plotting. It is interesting to note that scarlet fever 
cases plotted by ages on logarithmic probability paper also 
fall nearly on a straight line. 

The Mills-Reincke Phenomenon. — Problems like this 
offer excellent opportunities to apply the principles of 
statistics. In 1893-94 Mr. Hiram F. Mills found that at 
Lawrence, Mass., after the introduction of the sand filter to 
purify the public water-supply taken from the polluted 
Merrimac River, there was a material reduction in the 
general death-rate of the city. Notably typhoid fever was 
reduced, but this reduction was not sufficient to account 
for the fall in the general death-rate. About the same 
time Dr. J. J. Reincke found the same thing in Hamburg. 
In 1904 Hazen studied these and other records and stated 
that " where one death from typhoid fever had been avoided 
by the use of better water, a certain number of deaths, 
probably two or three, from other causes have been 
avoided." In 1910 Sedgwick and MacNutt ^ published an 
elaborate study in which Hazen's statement was dignified 
with the rank of "theorem." 

The natural inference from such statements is that the 
purification of a polluted water-supply reduces deaths from 
causes other than typhoid fever. In Lawrence if one con- 
siders short periods before and after the introduction of the 
filter a decrease is observed in several diseases, — as, for 
example, pneumonia, tuberculosis, cholera infantum and so 
on. Some have, without sufficient thought, extended the 

1 Sedgwick, W. T. and J. Scott MacNutt. On the Mills-Reincke 
Phenomenon and Hazen's Theorem. Jour. Infectious Diseases, Aug., 
1910, pp. 489-564. 



THE SANITARY INDEX 451 

idea back of Hazen's '^ theorem " to undue limits, and have 
argued that pure water has the effect of raising the gen- 
eral health, of lifting the health tone of individuals, and so 
has a value beyond that of preventing the spread of diseases 
of the intestinal tract. This is unwarranted and to that 
extent Dr. Chapin ^ has rightly criticized the '^ theorem." 
The idea may be correct, but the vital statistics available 
do not demonstrate it. The correlation between the de- 
creased typhoid-fever rate and the general death-rate in 
cities which have introduced water filtration or otherwise 
bettered their supply is not high. It is more frequently true 
where the original water-supply has been very badly pol- 
luted, as was the case at Lawrence. Even at Lawrence it is 
probable that the pneumonia death-rate was abnormally 
high just before the filter was built and that the reason 
for its subsequent decrease had little or nothing to do with 
water filtration. Yet to condemn the ^' theorem " al- 
together is to take too extreme a view. Without doubt 
infant mortality was reduced by filtration, chiefly through 
the reduction in diarrhoea] diseases. McLaughlin has 
shown that this has occurred in many places. 

The trouble with this whole problem has grown out of 
the use of general rates. If we want to find the effect of 
filtration we must compare the morbidity and mortality 
rates for particular diseases before and after filtration, with 
due regard to changes in population. Somebody who has 
time ought to restudy this whole matter in the light of 
recent data. 

The sanitary index. — Many attempts have been made 
to devise a '' sanitary index," to select and combine certain 
specific death-rates so as to get for a given place a single 
figure which, when compared with similar figures for other 
places, will correlate health and sanitary conditions. We 
1 Chapin, Chas. V., "Modes of Infection." 



452 A COMMENCEMENT CHAPTER 

know that the general death-rate will not serve this pur- 
pose. Even the death-rate adjusted to a standard popu- 
lation is inadequate. The infant mortality has been 
claimed as the best index. Dr. Wilmer R. Batt/ the 
Registrar of the Pennsylvania State Department of Health, 
has suggested a composite index which illustrates this 
striving to get an index. It is computed as follows : 

Sanitary index = 

Deaths from causes No. 1 to No. 15 plus all infant deaths 

Population 

The ratio of all the other deaths to the population is 
called the residual death-rate. Hence the sum of the two 
gives the general death-rate. 

He found that from 1906 to 1915 the general death-rate 
of the state declined from 16.0 to 13.8 per 1000 i.e., 13.8 
per cent. The " sanitary index/' however, declined from 
6.5 to 4.5, or 30.8 per cent, while the residual death-rate 
declined from 9.5 to 9.3 or only 2.1 per cent. This index, 
it will be observed, takes no account of the changing com- 
position of the population. 

Others have suggested that the index ought to be based 
on social and economic factors as well as vital statistics, 
and their point seems to be well taken. This only em- 
phasizes the complexity of the problem. The author be- 
lieves that it is too early to attempt the establishment of 
a health index, and that better results will be secured by 
the critical use of specific rates. 

Current use of vital statistics. — Vital statistics have 
their historic uses, but their greatest value lies in their 
immediate use. It is interesting and ultimately most val- 
uable to know that a baby has been born at a certain place, 
on a certain day, of such and such parentage, but it is more 

1 ?enn. Monthly Health Bulletin, No. 70, Feb., 1916. 



CURRENT USE OF VITAL STATISTICS 453 

important that the baby shall live and grow up well. No 
baby should be allowed to come unnoticed into the world; 
boards of health or other proper authorities should see to it 
that every baby born has a good chance to live. In most 
cases the parents, the physician and the nurse are sufficient 
caretakers and the public authorities should not be un- 
necessarily intrusive or over-zealous; on the other hand 
their advice and aid should be prompt where occasion war- 
rants, and immediate knowledge of the facts is the only 
basis of wise action. 

In reported cases of diseases dangerous to the public 
health the need for prompt action is even greater. It 
is by the daily study of such reports that pending epi- 
demics or local outbreaks of disease may be headed off. 
Every local health officer should keep on the walls of his 
office, or on a suitable frame, or in shallow drawers, a series 
of local maps — one for each important communicable dis- 
ease. The maps should show the names of the streets. 
There should be a street index at hand, with the street 
numbers given for each intersection, and with information 
as to which side of the street has the odd (or even) numbers. 
On these maps, with the aid of the index, each case of 
communicable disease should be marked with a pin imme- 
diately on receipt of the report. There are many little 
devices involving the use of pins of different colors for 
different dates, the removal of pins after recovery, the ad- 
ditions of pins to indicate death, and so on; the details of 
which are bound to vary according to local conditions. 
But the main thing is to study the pins daily. In the case 
of state departments of health the required maps are of 
course on a different scale and the cases are arranged by 
cities and towns instead of streets. Both local and state 
studies are necessary. 

In addition to the location maps the health officer needs 



454 A COMMENCEMENT CHAPTER 

to keep up chronological charts for each disease — a 
separate chart for each. Pins may be used for this work 
also, or lines may be drawn, black or colored. These 
charts, together with the maps, answer the questions 
where and when did the cases occur. M 

For state work another device is convenient, — namely, 
a summary of cases by cities, towns, or other geographical 
divisions, and by weeks or months. These should be made 
up regularly for comparison with past records. All cities 
have certain numbers of cases of communicable diseases 
which occur with a fair degree of regularity — and what 
the health officer needs most to know is whether there is at 
any time an abnormally large number of cases of any dis- 
ease. In order to quickly tell this he needs to have at 
hand certain generalized results of past experience. In 
New York City Dr. Bolduan has been in the habit of find- 
ing the average number of cases of typhoid fever, for ex- 
ample, in each ward and for each week of the year, — but 
omits from these averages any local outbreak or epidemics. 
He has called this the " normalized average." ^ In the 
author's opinion what is needed here is not the average, 
with the unusual conditions omitted, but the median. 
The Massachusetts State Department of Health is using 
the median under the name of the " endemic index." A 
better name would be the endemic median. This can be 
very easily found for a five- or ten-year period and would 
serve admirably as a standard of comparison. It would 
of course need occasional revision. 

Card systems are generally found most convenient for 
keeping records of individual reports, and the punched- 
card system with mechanical devices for sorting and count- 
ing is the best of all. 

. 1 Bolduan, Chas. Ii^., Typhoid Fever in New York City, No. 3 
Monograph Series, Aug., 1912. 



PUBLICATION OF REPORTS 455 

Publication of reports. — The author will perhaps be 
regarded as a heretic on the subject of published reports. 
He believes, however, that thousands of pages of useless 
tables of reported cases of disease are printed every year in 
the United States at enormous expense and that the same 
amount of money spent in maintaining more complete and 
more accurate records in state and local health departments 
and in studying and using the records from day to day 
would bring better results. The object of reporting dis- 
eases dangerous to the public health is not to pile up 
records but to prevent the diseases from spreading. State- 
ments of the occurrences of communicable diseases pub- 
Ushed monthly, or even weekly, usually reach their readers 
too late to be of any practical use, while as historical 
records such frequent publication is wholly unnecessary. 
Some publication is desirable, however, but only that which 
is of real use. 

Let us consider the case of communicable diseases, for 
example, as reported to a state department of health. If 
the number of cases of measles in a city is less than the 
endemic median, that is, less than the ordinary number 
of cases, no announcement is necessary; but should the 
number of cases rise above the endemic median a prompt 
announcement of that fact in the local paper ^ might be 
of positive benefit as it would sound a warning. If the 
fire bells were ringing very gently all the time except when 
a fire occurred and then rang loudly, the public would not 
heed the warning; and in the same way the constant pub- 
hcation of figures which are of little moment blunts the 
sense of caution. Arrangements might well be made, how- 
ever, for the immediate publication of notices of all unusual 
occurrences of disease in local papers or wherever such 
notices would do the most good. So far as communicable 

^ Daily paper preferred, 



456 A COMMENCEMENT CHAPTER 

diseases are concerned the general principle of publication 
should be to publish at once or not at all and to publish 
only the unusual occurrences. The preparation of such 
notices would by reflex action stimulate the health officers 
themselves, and would assist physicians in making diagnosis 
of suspected cases. 

The problem of annual reports is different. Here the 
object is to establish a record for permanent preservation, 
useful alike to health officers, to physicians, and to the in- 
terested public. The calendar year with its subdivisions 
is the most convenient unit of time. The vital statistics 
of every political subdivision in the country should be 
published annually, and as soon after the end of the year 
as possible. Here we find a great amount of unnecessary 
duplication. It is a waste of money to have the local 
Board of Health of Cambridge, Mass., publish certain facts 
(usually a year or two late), to have the same facts pub- 
lished by the State Registrar and perhaps by the State De- 
partment of Health, and finally to have them published 
again by the U. S. Bureau of the Census, and perhaps by 
the U. S. Public Health Service. It is worse than waste- 
ful, because the various tables often fail to agree and all 
sorts of distressing statistical errors creep in. On the other 
hand, while the figures for Cambridge may be found in 
several places, there may be other places where it is diffi- 
cult to find any statistics at all. Uniformity in this matter 
is very greatly needed^ and this must come through federal 
control or state cooperation, with uniform minimum 
schedules to serve as a basis of record. 

The author believes that no systematic attempt should 
be made every year to publish specific rates or minute 
analyses of rates, for the reason that such studies are based 
necessarily on estimated populations. Such studies are of 
course very necessary for the study of special problems as 



PUBLICATION OF REPORTS 457 

they arise, but these results should be published as special 
studies and not as a part of a systematic schedule. It 
would be better to wait for the census years, when the 
facts of population can be used instead of estimates and to 
then make a most careful analysis of all vital statistics. 
Such an analysis made once in five years in Massachusetts 
would serve every useful purpose, would save much time 
and expense, would avoid the need of revision and would 
prevent the publication of figures which contain annoying 
variations. The principle should be to wait for the facts, 
and then make a careful analysis based on the facts. Of 
course, general rates should be published annually, based 
on estimated populations, but no one need take these very 
seriously, as in any event they mean little. If it is thought 
worth while to publish specific rates for each post censal 
year, these should be recomputed after the next census has 
been taken. 

Various attempts to establish standards have been made. 
One of these may be found in the American Journal of 
Public Health. 1 Another in the annual report of the N. Y. 
State Department of Health for 1912, another in the 
Quarterly Publication of the American Statistical Associa- 
tion 2 and so on. In establishing standards it will be neces- 
sary to determine what shall be the geographical units, 
what subdivision of the year, what data and in what com- 
binations. The usual facts secured in regard to deaths are 
(1) place of death, (2) time of death, (3) sex, (4) age, 
(5) race or color, (6) cause of death, (7) birthplace, (8) 
birthplace of father, (9) birthplace of mother, (10) marital 
condition, (11) occupation. The possible number of com- 
binations of these eleven items two at a time is 55, three at 
a time 165, and four at a time 330. No wonder therefore 
that there is lack of uniformity in published reports. Any 
1 1913, p. 595. 2 1911, p. 510. 



458 A COMMENCEMENT CHAPTER 

standard tables must of necessity be arbitrary. The time 
has come when uniformity of report is necessary in the in- 
terest of both economy and efficiency. 

EXERCISES AND QUESTIONS 

1. Distinguish between the environments represented by the follow- 
ing terms: 

a. A felt hat and a straw hat factory. 

6. A paper box and a wooden box factory. 

c. An iron and a brass foundry. 

d. A wholesale and a retail merchant or dealer. 

e. A farm laborer on his home farm and one working out. 
/. A clerk in a store and a salesman. 

g. A dressmaker in a factory or shop and one working elsewhere. 

h. A cook and a servant. 

^. A paid housekeeper and a servant girl. 

J. A practical and a trained nurse, 

2. To what extent do these terms conceal other important differ- 
ences in age or sex or nationality? 

3. What data were collected in the industrial clinic of the Massa- 
chusetts General Hospital? [Monthly Review (Dec, 1917), U. S. 
Bureau of Labor Statistics. Edsall, David J.: The Study of Occupa- 
tional Diseases in Hospitals.] 

4. How would you explain the alleged fact that more cases of in- 
fectious diseases are reported to the New York City Department of 
Health on Monday than on any other day, and the fewest on Saturday? 

5. How are the medical and vital statistics of the U. S. Navy kept? 
[See Am. J. P. H., June, 1918, p. 442.] 

6. How are the medical and vital statistics of the U. S. army kept^ 
[See Am. J. P. H., Jan., 1918, p. 14.] 

7. What facts are needed in the registration of still-births? [See 
Am. J. P. H., Jan., 1917, p. 46.] 

8. Describe the epidemic of poliomyelitis in New York and New 
England in 1916. [See Am. J. P. H., Feb., 1917, p. 117.] 

9. What proportion of children "take" the common children's 
diseases at some time? [See Am. J. P. H., Sept., 1916, p. 971.] 



APPENDIX I 
REFERENCES 

To study demography, or even vital statistics, seriously 
one must have at hand several of the standard textbooks 
on the statistical method, and certain of the more recent 
federal, state and municipal reports. One must also have 
access to files of certain periodicals. The following is a 
list of some of the more important of these references. It 
is far from being complete, and is intended merely to pave 
the way for further searches in the library. 

A complete list of references to books and articles on the 
many phases of the subject would be overwhelming. The 
most recent writings on vital statistics are not necessarily 
the best for the beginner to study, as some of the soundest 
and most logical monographs were written many years ago. 
Of course, the most recent data are the most interesting — 
but that is another matter. 

Many references to particular articles will be found 
scattered through the footnotes of this book and printed in 
connection with the Exercises and Questions. 

GENERAL TEXTBOOKS. 

Newsholme, Arthur. Elements of Vital Statistics. Macmillan 
Co., 1899. 

BowLEY, Arthur L. Elements of Statistics. New York, Scribners, 
1907. 

BowLEY, Arthur L. An Elementary Manual of Statistics. Lon- 
don, MacDonald and Evans, 1910. 

Elderton, W. Palin and Ethel M. Elderton. Primer of Statis- 
tics. New York, Macmillan Co. 

459 



460 APPENDIX I 

King, Wellford J. The Elements of Statistical Method. New 

York, Macmillan Co., 1912. 
Trask, John W. Vital Statistics — a report published by the 

U. S. Public Health Service, Apr. 3, 1914. 
Yule, G. Udny. Introduction to the Theory of Statistics. London, 

Griffin & Co., 1912. 
Whipple, George C. Typhoid Fever. New York, John Wiley & 

Sons, Inc. ,1908. 
KoREN, John. History of Statistics. New York, Macmillan Co., 

1918. 

PERIODICALS. 

American Statistical Association. Quarterly Publications. Vol. 

I in 1888. 
American Journal of Public Health. Monthly. The official' 

publication of the American Public Health Association. 
Public Health Reports. Weekly. Published by the U. S. Public 

Health Service. 
U. S. Bureau of Labor Statistics. Monthly Review. 
Journal op the Royal Statistical Society. 

ANNUAL, MONTHLY AND WEEKLY REPORTS. 

There are scores of annual reports which ^eal with vital 
statistics. The following are illustrative: 

U. S. Bureau of the Census. Mortality Statistics. Annually 
since 1900. 

England and Wales. Annual reports of Registrar-General. (79th 
report in 1916.) 

Massachusetts State Registration Reports. Annually since 
1842. 

Massachusetts State Board of Health (now Department of 
Health). Annually since 1870. 

State Departments of Health of New York, New Jersey, Penn- 
sylvania, Ohio, Michigan, Maine, New Hampshire, Connecticut, 
etc. 

Annual Reports of Boards of Health of New York City, Boston, 
Philadelphia, Chicago, Providence, etc. 

Some boards of health publish monthly reports — New York, Massa- 
chusetts, Ohio, etc. 

Some city health departments publish weekly reports — New York, 
Chicago, etc. 



APPENDIX I 461 

DEMOGRAPHY. 

Statistique Generale de la France. Statistique Internationale 
du Mouvement de la Population d'apres les registres d'etat civil, 
1907, 1913. 

Westergaard, Harold. Die Lehre von der Mortalitat und Mor- 
bilitat, anthropologisch-statistische Untersuchungen. Jena. 
Gustav Fischer, 1901. 

Graunt, Capt. John. Natural and Political Observations based 
upon Bills of Mortality. 1662. (Historical value.) 

Chadwick, Edwin. Health of Nations. (Historical value.) 

Farr, William. Vital Statistics — a memorial volume of selec- 
tions from his reports and writings. Edited by Noel A. Hum- 
phreys, London. Office of the Sanitary Institute. 

Meitzen, Dr. August. History Theory and Technique of Statis- 
tics. Translated by Dr. Roland P. Falkner. Annals of the Am. 
Acad, of Political and Social Science, 1891. 

Pearson, Karl. Life, Letters and Labors of Sir Francis Galton, 
Vol. I. Cambridge, England, University Press, 1914. 

Bailey, Wm. B. Modern Social Conditions. New York, Century 
Co., 1906. 

ARITHMETIC. 

West, Carl S. Introduction to Mathematical Statistics. Colum- 
bus, R. G. Adams & Co., 1918. 

Bailey, W, B. and Joseph Cummings. Statistics. Chicago, A. C. 
McClurg Co., 1917. 

Westergaard, Harold. Scope and Methods of Statistics. Quar. 
Pub. Am. Sta. Asso., XV, 1916, pp. 225-291. 

Secrist, Horace. Introduction to Statistical Methods. New 
York, Macmillan Co., 1917. 

Saxelby, F. M. a Course in Practical Mathematics. London, 
Longmans, Green & Co., 1908. 

Thompson, Sylvanus P. Calculus Made Easy. London, Mac- 
millan Co., 1917. 

GRAPHICS. 

Reinhardt, Chas. W. Lettering for Draftsmen, Engineers and 
Students. New York, D. Van Nostrand Co., 1909. 

Peddle, John B. The Construction of Graphical Charts. New 
York, McGraw-Hill Co., 1910. 



462 APPENDIX I 

Brinton, Willard C. Graphic Methods for Presenting Facts. 

New York, Engineering Magazine Co., 1914. 
Fisher, Irving. The Ratio Chart. Quar. Pub. Am. Sta. Asso., 

1917, p. 577. 

CENSUS — REGISTRATION. 

Wilbur, Cressy L. The Federal Registration Service of the United 

States : its development, problems and defects. U. S. Bureau of 

the Census, 1916. 
Newsholme, Arthur. . A National System of Notification and 

Registration. Jour. Royal. Sta. Soc, Vol. 59, p. 1, 1896. 
DuRAND, E. Dana. Changes in Census Methods for the Census of 

1910. Am. Jour, of Sociology, 1910. 
U. S. Bureau of the Census. American Census Taking from the 

First Census of the United States, 1908. 
U. S. Bureau of the Census. Index to Occupations, alphabetical 

and classified, 1915. 



POPULATION. 

United States Census, 1790-1900. Comprehensive reports, 

usually in several volumes, published every ten years. 
U. S. Bureau of the Census. 1910. Population, Vols. I, II and 

III. 
U. S. Bureau of the Census. Annual Estimates of Population, 

are published in a series of bulletins. Bulletin 133, for 

1916. 
U. S. Bureau of the Census. A Century of Population Growth, 

1790-1900. Pub. in 1909. 
Massachusetts State Census. Intermediate between federal 

censuses since 1845. [Last published report in 1905; report for 

1915 in preparation.] 
Leroy-Beaulieu, p. The Influence of Civilization on the Move- 
ment of Population. Jour. Royal Sta. Soc, Vol. 54, 1891. 
Franklin, Benjamin. Observations concerning the Increase of 

Mankind. Book, Philadelphia, 1751. 
Jarvis, E. History of the Progress of Population of the United 

States. Book, Boston, 1877. 
Bailey, W. B. Modern Social Conditions. N. Y., Century Co., 

1906. 



APPENDIX I 463 

:>ENERAL-RATES. 

Newsholme, a. The Declining Birth-rate. New York, Moffat, 

Yard & Co., 1911. 
U. S. Bureau of the Census. Birth Statistics. First annual report 

in 1915. 
Humphreys, N. A. Value of the Death-rate as a Test of Sanitary 

Conditions. Jour. Royal Statistical Society, Vol. 37, 1874. 
Yule, G. M. On the Changes in the Marriage and Birth-rates in 

England and Wales during the past Half Century. Jour. Royal 

Sta. Soc, Vol. 69, p. 88, 1906. 

SPECIFIC RATES. 

Pearson, Karl, Alice Lee and Ethel M. Elderton. On the 
Correction of Death-rates, 1910. 

GuiLFOY, Wm. H. The Death-rate of New York as affected by the 
Cosmopolitan Character of its Population. Quar. Pub. Am. 
Sta. Asso., 1907. 

Andrew, J. Grant. Age Incidence, Sex and Comparative Fre- 
quency in Disease. London, Bailliere, Tindall & Cox, 1909. 

CAUSES OF DEATH. 

A. P. H. a. Committee Report. The Accuracy of Certified Causes 
of Death. Pubhc Health Reports, Sept. 28, 1917, pp.'1557-1632. 

U. S. Bureau of the Census. Manual of the International List 
of Causes of Death, 1911. 

U. S. Bureau of the Census. Index of Joint Causes of Death, 1914. 

U. S. Bureau of the Census. Physicians' Pocket Reference to the 
International List of Causes of Death, 1918. 

PROBABILITY. 

Davenport, Chas. B. Statistical Methods, with Special Reference 

to Biological Variations. Second edition, New York, John Wiley 

and Sons, Inc., 1904. 
Fisher, Arne. The Mathematical Theory of Probabilities. New 

York, Macmillan Co., 1915. 
Whipple, George C. The Element of Chance in Sanitation. Jour. 

Franklin Institute, July and Aug., 1916. 
Weld, LeRoy D. Theory of Errors and Least Squares. New York, 

Macmillan Co., 1916. 



464 APPENDIX I 

Goodwin, A. M. Elements of the Preoision of Measurements and 
Graphical Methods. New York, McGraw-Hill Co., 1913. 

La Place, P. S., Marquis de. Theorie analyiique des probabilites, 
1814. (Historical value.) 

QuETELET, L. A. S. Lettres sur la theorie des probabilites, appli- 
quee aux sciences morales et politiques, 1846. (English trans- 
lation by O. G. Downs, 1849.) 

Brownlee, John. The Mathematical Theory of Random Migra- 
tion and Epidemic Distribution. Proc. Royal Soc. of Edin- 
burgh, Vol. 31, p. 262, 1910-11. 

CORRELATION. 

Jevons, W. Stanley. The Principles of Science. London, Mac- 

millan Co., 1907. 
Pearson, Karl, Alice Lee and Ethel M. Elderton. On the 

Correlation of Death-rates. Jour. Royal Sta. Soc, Vol. 73, 

p. 534, 1910. 

LIFE TABLES. 

MoiR, Henry. Life Assurance Primer. New York, The Spectator 

Co., 1912. 
' Henderson, Robert. Mortality Laws and Statistics. New York. 

John Wiley & Sons, Inc., 1915. 
Glover, Jas. W. United States Life Tables, 1910. U. S. Census, 

1916. 
Burn, Joseph. Vital Statistics Explained. London, Constable and 

Company, Ltd., 1914. 



APPENDIX II 

THE MODEL STATE LAW FOR MORBIDITY REPORTS 

ADOPTED BY THE ELEVENTH ANNUAL CONFERENCE OF STATE AND TERRI- 
TORLA.L HEALTH AUTHORITIES WITH THE UNITED STATES PUBLIC 
HEALTH SERVICE, MINNEAPOLIS, JUNE 16, 1913. 

A Bill To provide for the notification of the occurrence and prevalence of certain diseaeeB. 

Be it enacted by the Senate and General Assembly of the State of : 

Section 1. It shall be, and is hereby, made the duty of the State 
department of health (or commissioner or board of health) to keep 
currently informed of the occurrence, geographic distribution, and 
prevalence of the preventable diseases throughout the State, and for 
this purpose there shall be established in the State department of health 
a bureau (or division) of sanitary reports which shall, under the direc- 
tion of the State commissioner of health (State health officer or secre- 
tary of the State board of health), be in charge of an assistant com- 
missioner of health who shall receive an annual salary of dollars 

and the necessary expenses incurred in the performa,nce of his duties. 
The State department of health shall provide such clerical and other 
assistance as may be necessary for the establishment and maintenance 
of said bureau. 

Sec. 2. The following-named diseases and disabilities are hereby 
made notifiable and the occurrence of cases shall be reported as herein 
provided : 

GROUP I. — INFECTIOUS DISEASES 

Actinomycosis. Dengue. 

Anthrax. • Diphtheria. 

Chicken-pox. Dysentery: 
Cholera. Asiatic (also cholera nos- (a) Amebic. 

tras when Asiatic cholera is pres- (6) Bacillary. 

ent or its importation threatened). Favus. 

Continued fever lasting seven days. German measles. 

465 



466 



APPENDIX II 



GBOUP I. — INFECTIOUS DIS- 
EASES — Continued 

Glanders. 

Hookworm disease. 

Leprosy. 

Malaria. 

Measles. 

Meningitis: 

(a) Epidemic cerebrospinal. 
(6) Tuberculous. 
Mumps. 

Ophthalmia neonatorum (conjunc- 
tivitis of new born infants) . 
Paragonimiasis (endemic hemoptysis) . 

Paratyphoid fever. 

Plague. 

Pneumonia. 

Poliomyelitis (acute infectious). 

Rabies. 

Rocky Mountain spotted, or tick, 
fever. 

Scarlet fever. 

Septic sore throat. 

Smallpox. 

Tetanus. 

Trachoma. 



Typhus fever. 
Whooping cough. 
Yellow fever. 



GROUP II. — aCCUPATIONAL DIS- 
EASES AND INJURIES. 

Arsenic poisoning. 
Brass poisoning. 
Carbon monoxide poisoning. 
Lead poisoning.' 
Mercury poisoning. 
Natural gas poisoning. 
Phosphorous poisoning. 
Wood alcohol poisoning. 
Naphtha poisoning. 
Bisulphide of carbon poisoning. 
Dinitrobenzine poisoning. 
Caisson disease (compressed-air 

illness) . 
Any other disease or disability 

contracted as a result of the 

nature of the person's employ-. 

ment. 

GROUP III. — VENEREAL DISEASES 

Gonococcus infection. 
Syphilis. 



Trichinosis. • ^^^ 

Tuberculosis (all forms, the organ or group iv.- diseases op un- 

part affected in each case to be ^^own origin. 

specified). PeUagra. 

Typhoid fever. Cancer. . 

Provided, That the State department of health (or board of health) 
may from time to time, in its discretion, declare additional diseases 
notifiable and subject to the provisions of this act. 

Sec. 3. Each and every physician practicing in the State of 
who treats or examines any person suffering from or afflicted with, or 
suspected to be suffering from or afflicted with, any one of the notifiable 
diseases shaU immediately report such case of notifiable disease m writ- 
ing to the local health authority having jurisdiction. Said report shall 



APPENDIX II 467 

be forwarded either by mail or by special messenger and shall give the 
following information: 

1. The date when the report is made. 

2. The name of the disease or suspected disease. 

3. The name, age, sex, color, occupation, address, and school attended 
or place of employment of patient. 

4. Number of adults and children in the household. 

5. Source or probable source of infection or the origin or probable 
origin of the disease. 

6. Name and address of the reporting physician. 

Provided, That if the disease is, or is suspected to be, smallpox the 
report shall, in addition, show whether the disease is of the mild or 
virulent type and whether the patient has ever been successively 
vaccinated, and, if the patient has been successfully vaccinated, the 
number of times and dates or approximate dates of such vaccination; 
and if the disease is, or is suspected to be, cholera, diphtheria, plague, 
scarlet fever, smallpox, or yellow fever, the physician shall, in addition 
to the written report, give immediate notice of the case to the local 
health authority in the most expeditious manner available; and if the 
disease is, or is suspected to be, typhoid fever, scarlet fever, diphtheria 
or septic sore throat the report shall also show whether the patient has 
been, or any member of the household in which the patient resides is, 
engaged or employed in the handling of milk for sale or preliminary to 
sale: And provided further, That in the reports of cases of the venereal 
diseases the name and address of the patient need not be given. 

Sec. 4. The requirements of the preceding section shall be applicable 
to physicians attending patients ill with any of the notifiable diseases 
in hospitals, asylums, or other institutions, public or private : Provided, 
That the superintendent or other person in charge of any such hospital, 
asylum, or other institution in which the sick are cared for may, with 
the written consent of the local health officer (or board of health) having 
jurisdiction, report in the place of the attending physician or physicians 
the cases of notifiable diseases and disabilities occurring in or admitted 
to said hospital, asylum, or other institution in the same manner as that 
prescribed by physicians. 

Sec. 5. Whenever a person is known, or is suspected, to be afflicted 
with a notifiable disease, or whenever the eyes of an infant under two 
weeks of age become reddened, inflamed, or swollen, or contain an 
unnatural discharge, and no physician is in attendance, an immediate 
report of the existence of the case shall be made to the local health officer 



468 APPENDIX II 

by the midwife, nurse, attendant, or other person in charge of the 
patient. 

Sec. 6. Teachers or other persons employed in, or in charge of, pubHc 
or private schools, including Sunday Schools, shall report immediately 
to the local health officer each and every laiown or suspected case of a 
notifiable disease in persons attending "or employed in their respective 
schools. 

Sec. 7. The written reports of cases of the notifiable disease required 
by this act of physicians shall be made upon blanks supplied for the 
purpose, through the local health authorities, by the State department 
of health. These blanks shall conform to that adopted and approved 
by the State and Territorial health authorities in conference with the 
United States Public Health Service. 

Sec. 8. Local health officers or boards of health shall within seven 
days after the receipt by them of reports of cases of the notifiable 
diseases forward by mail to the State department of health the original 
written reports made by physicians, after first having transcribed the 
information given in the respective reports in a book or other form of 
record for the permanent files of the local health office. On each report 
thus forwarded the local health officer shall state whether the case to 
which the report pertains was visited or otherwise investigated by a 
representative of the local health office . and whether measures were 
taken to prevent the spread of the disease or the occurrence of addi- 
tional cases. 

Sec. 9. Local health officers or boards of health shall, in addition to 
the provisions of section 8, report to the State department of health in 
such manner and at such times as the State department of health may 
require by regulation the number of new cases of each of the notifiable 
diseases reported to said local health officers or boards of health. 

Sec. 10. Whenever there occurs within the jurisdiction of a local 
health officer or board of health an epidemic of a notifiable disease, the 
local health officer or board of health shall, within 30 days after the ' 
epidemic shall have subsided, make a report to the State departnient of 
health of the number of cases occurring in the epidemic, the number of 
cases terminating fatally, the origin of the epidemic, and the means by 
which the disease was spread: Provided, That whenever the State 
department of health has taken charge of the control and suppression or 
undertaken the investigation of the epidemic, the local health authority 
having jurisdiction need not make the report otherwise required. 

Sec. 11. No person shall be appointed to the position of local health 



APPENDIX II 469 

officer in any city, town, or county until after the qualifications of said 
person have been approved by the State department of health. 

Sec. 12. In localities in which there are no local health officers or 
boards of health, and in localities in which, although there are health 
officers or boards of health, adequate provision has not, in the opinion 
of the State department of health, been made for the proper notification, 
investigation, and control of notifiable disease, and in localities in which 
the local health authorities fail to carry out the provisions of this act, 
the State department of health shall appoint properly qualified sanitary 
officers to act as local health officers and to prevent the spread of disease 
in and from such localities and to enforce the provisions of this act: 
Provided, That salaries and other expenses incurred mider the provisions 
of this section shall be paid by the local authorities. 

Sec. 13. Any physician or other person or persons who shall fail, 
neglect or refuse to comply with, or who shall violate any of the pro- 
visions of this act shall be guilty of a misdemeanor, and upon conviction 

thereof shall be sentenced to pay a fine of not less than dollars 

nor more than dollars or to imprisonment for not less than 

days nor more than days for each offense : Provided, That in the 

case of a physician his license to practice medicine within .the State may 
be revoked in accordance with existing statutory provisions. 

Sec. 14. No license to practice medicine shall be issued to any person 
until after the applicant shall have filed with the State licensing board 
a statement, signed and sworn to before a notary or other officer quali- 
fied to administer oaths, that said applicant has familiarized himself 
with the requirements of this act, a copy of which sworn statement shall 
be forwarded to the State department of health. 

Sec. 15. Each and every person engaged in the practice of medicine 
shall display in a prominent place in his or her office a card upon which 
sections 2, 3, 4, 7, 13, 14, and 15 of this act have been printed with type 
not smaller than 10-point. A similar card shall be displayed in a prom- 
inent place in the office of each and every hospital, asylum, or other 
public or private institution for the treatment of the sick. These cards 
shall each be not less than 1 square foot in size and shall be furnished 
to institutions and licensed physicians without cost by the State de- 
partment of health. 

Sec. 16. The sum of dollars is hereby appropriated from any 

money in the State treasury not otherwise appropriated for carrying 
out the provisions of this act. 

Sec. 17. This act shall take effect immediately, and all acts or parts 
of acts inconsistent with the provisions of this act are hereby repealed. 



470 



APPENDIX II 



THE STANDARD MORBIDITY NOTIFICATION BLANK 

The followiDg model notification blank was also adopted by the conference of state and 
territorial health authorities with the United States Public Health Service, June 16, 1913, 
as the standard notification blank referred to in section 7 of the Model Law as the one to 
be used in the reporting of cases of the notifiable diseases. This blank is intended to be 
printed on a post card: 

[Face of card.] 



,, 191. 



(Date.) 

Disease or suspected disease 

Patient's name , age , sex color 

Patient's address , occupation 

School attended or place of employment 

Number in household: Adults , children 

Probable source of infection or origin of disease 

If disease is smallpox, type , number of times 

successfully vaccinated and approximate dates 

If typhoid fever, scarlet fever, diphtheria, or septic sore throat, was patient, or is any 

member of household engaged in the production of handling of milk 

Address of reporting physician 

Signature of physician 



[Reverse of card.] 



For use of local health department. 



3 •§ : 








B i $': 


^: 


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APPENDIX II 471 

HOSPITAL DISCHARGE CERTIFICATE 

Suggested by Bolduan for use in connection with, hospital morbidity reports. 
DISCHARGE CERTIFICATE. 



Name of hospital Hospital admission No. 

Sex Age 

How admitted — Ambulance 



or White. Hebrew, 

own application Colored. Gentile. 

or Mongolian. 

(Tabulation transfer from 



No.) other hospital. Place of birth . 



Patient's address Single or married or widowed or divorced or 

Borough unknown. 

Date admitted Discharged to — 

Date discharged Home. 

Days in hospital months Other hospital. 

days Convalescent retreat. 

(If over a year, omit the days and give only Coroner. 

years and months.) 
Occupation — (a) Trade, profession, or particular kind of work. 

(6) General . nature of the industry, business, or establishment in which 
employed (or employer). 

Diagnosis 

and 

Complications 

If operated upon, state nature of operation 

Condition on discharge: Cured. Improved. Unimproved. 

Died — Autopsy. 

No autopsy. 

Signed 

House Physician — Surgeon. 



APPENDIX III 

THE MODEL STATE LAW FOR THE REGISTRATION OF 
BIRTHS AND DEATHS 

A. Bill 1 To provide for the registration of all births and deaths in the State of . 



Note. — After the bill has been prepared for presentation to the legislature of a State, 
the title should be carefully revised by competent legal authority. 

Be it enacted by the legislature of the State of — ■- 



Section 1. That the State board of health shall have charge of the 
registration of births and deaths; shall prepare the necessary instruc- 
tions, forms, and blanks for obtaining and preserving such records and 
shall procure the faithful registration of the same in each primary regis- 
tration district as constituted in section 3 of this act, and in the central 
bureau of vital statistics at the capital of the State. The said board 
shall be charged with the uniform and thorough enforcement of the law 
throughout the State, and shall from time to time recommend any 
additional legislation ^ that may be necessary for this purpose. 

Sec. 2. That the secretary of the State board of health shall have 
general supervision over the central bureau of vital statistics, which is 
hereby authorized to be established by said board, and which shall be 
under the immediate direction of the State registrar of vital statistics, 
whom the State board of health shall appoint within thirty days after 
the taking effect of this law, and who shall be a medical practitioner of 
not less than fiv6 years' practice in his profession, and a competent vital 
statistician. The State registrar of vital statistics shall hold office for 
four years and until his successor has been appointed and has qualified, 
unless such office shall sooner become vacant by death, disquahfication, 

1 Before introducing this bill in any legislature it should be carefully 
redrafted by a competent lawyer and submitted to the Bureau of the 
Census for criticism. 

2 The words "and shall promulgate any additional rules or regula- 
tions" may be inserted in bills prepared for States in which the State 
board of health has power to make rules and regulations having the 
effect of law. 

472 



APPENDIX III 473 

operation of law, or other causes. Any vacancy occurring in such 
office shall be filled for the unexpired term by the State board of health. 
At least ten days before the expiration of the term of office of the State 
registrar of vital statistics, his successor shall be appomted by the State 
board of health. The State registrar of vital statistics shall receive an 

annual salary at the rate of dollars from the date of his entering 

upon the discharge of the duties of his office. The State board of health 
shall provide for such clerical and other assistants as may be necessary 
for the purposes of this act, who shall serve during the pleasure of thet 
board, and shall fix the compensation of persons thus employed within 
the amount appropriated, therefor by the legislature. The custodian 
of the capitol shall provide for the bureau of vital statistics in the State 

capitol at suitable offices, which shall be properly equipped with 

fireproof vault and filing cases for the permanent and safe preservation 
of all official records made and returned under this act. 

Sec. 3. That for the purposes of this act the State shall be divided 
into registration districts as follows: Each city, each incorporated 
town, and each township ^ shall constitute a primary registration dis- 
trict : Provided, That the State board of health may combine two or more 
primary registration districts when necessary to facilitate registration. 

Sec. 4. That within ninety days after the taking effect of this act, or 
as soon thereafter as possible, the State board of health shall appoint 
a local registrar of vital statistics for each registration district in the 
State. 2 The term of office of each local registrar so appointed shall be 

^ Or other primary political unit, as "town," "precinct," "civil 
district," "hundred," etc. When there are no such units available, the 
following substitutes for section 3 may be employed: Section 3. That 
for the purposes of this act the State shall be divided into registration 
districts as follows: Each city and each incorporated town shall con- 
stitute a primary registration district; and for that portion of each 
county outside of the cities and incorporated towns therein the State 
board of health shall define and designate the boundaries of a sufficient 
number of rural registration districts, which districts it may change or 
combine from time to time as may be necessary to insure the convenience 
and completeness of registration. 

2 This method of appointment of local registrars by the State board 
of health — or perhaps by the State registrar or upon his nomination — 
with a reasonably long term of service and subject to removal for neglect 
of duty, is the preferable one for efficient service. Should there be 
objection, however, to the creation of new offices, the section may be 
redrafted so that it will provide that township, village, or city clerks, or 
other suitable ojBficials, shall be the local registrars. 



474 APPENDIX III 

four years, and until his successor has been appointed and has qualified, 
unless such office shall sooner become vacant by death, disqualification, 
operation of law, or other causes: Provided, That in cities where health 
officers- or other ofiicials are, in the judgment of the State board of 
health, conducting effective registration of births and deaths under 
local ordinances at the time of the taking effect of this act such officials 
may be appointed as registrars in and for such cities, and shall be 
subject to the rules and regulations of the State registrar and to all of 
the provisions of this act. Any vacancy occurring in the office of local 
registrar of vital statistics shaU be filled for the unexpired term by the 
State board of health. At least ten days before the expiration of the 
term of office of any such local registrar his successor shall be appointed 
by the State board of health. 

Any local registrar who, in the judgment of the State board of health, 
fails or neglects to discharge efficiently the duties of his office as set forth 
in this act, or to make prompt and complete returns of births and deaths 
as required thereby, shall be forthwith removed by the State board of 
health, and such other penalties may be imposed as are provided under 
section 22 of this act. 

• Each local registrar shall, immediately upon his acceptance of ap- 
pointment as such, appoint a deputy, whose duty it shall be to act in 
his stead in case of his absence or disability; and such deputy shall in 
writing accept such appointment and be subject to all rules and regula- 
tions governing local registrars. And when it appears necessary for the 
convenience of the people in any rural district the local registrar is 
hereby authorized, with the approval of the State registrar, to appoint 
one or more suitable persons to act as subregistrars, who shall be author- 
ized to receive certificates and to issue burial or removal permits in and 
for such portions of the district as may be designated; and each sub- 
registrar shall note on each certificate, over his signature, the date of 
filing, and shall forward all certificates to the local registrar of the 
district within ten days, and in all cases before the third day of the 
following month: Provided, That each subregistrar shall be subject to 
the supervision and control of tne State registrar and may be by him 
removed for neglect or failure to perform his duty in accordance with the 
provisions of this act or the rules and regulations of the State registrar, 
and shall be subject to the same penalties for neglect of duty as the local 
registrar. 

Sec. 5. That the body of any person whose death occurs in this 
State, or which shall be founTl dead therein, shall not be interred, de- 
posited in a vault or tomb, cremated or otherwise disposed of, or re- 



APPENDIX III , 475 

moved from or into any registration district, or be temporarily held 
pending f mother disposition more than seventy-two hours after death, 
unless a permit for burial, removal, or other disposition thereof shall 
have been properly issued by the local registrar of the registration 
district in which the death occurred or the body was found. ^ And no 
such burial or removal permit shall be issued by any registrar until, 
wherever practicable, a complete and satisfactory certificate of death 
has been filed with him as hereinafter provided: Provided, That when 
a dead body is transported from outside the State into a registration 

district in for burial, the transit or removal permit, issued in 

accordance with the law and health regulations of the place where the 
death occurred, shall be accepted by the local registrar of the district 
into which the body has been transported for burial or other disposition, 
as a basis upon which he may issue a local burial permit; he shall note 
upon the face of the burial permit the fact that it was a body shipped in 
for interment, and give the actual place of death; and no local registrar 
shall receive any fee for the issuance of burial or removal permits under 
this act other than the compensation provided in section 20. 

Sec. 6. That a stillborn child shall be registered as a birth and also 
as a death, and separate certificates of both the birth and the death 
shall be filed with the local registrar, in the usual form and manner, the 
certificate of birth to contain in place of the name of the child, the word 
"stillbirth": Provided, That a certificate of birth and a certificate of 
death shall not be required for a child that has not advanced to the fifth 
month of uterogestation. The medical certificate of the cause of death 
shall be signed by the attending physician, if any, and shall state the 
cause of death as "stillborn," with the cause of the stillbirth, if known, 
whether a premature birth, and, if born prematurely, the period of 
uterogestation, in months, if known; and a burial or removal permit 
of the prescribed form shall be required. Midwives shall not sign 
certificates of death for stillborn children; but such cases, and still- 
births occurring without attendance of either physician or midwife, 
shall be treated as deaths without medical attendance, as provided for 
in section 8 of this act. 

Sec. 7.* That the certificate of death shall contain the following 
items, which are hereby declared necessary for the legal, social, and 
sanitary purposes subserved by registration records ! ^ 

1 A special proviso may be required for sparsely settled portions of 
a State. 

2 The following items are those of the United States standard certi- 
ficate of death, approved by the Bureau of the Census. 



476 APPENDIX ill 

(1) Place of death, including State, county, township, village, or 
city. If in a city, the ward, street, and house number; if in a hospital 
or other institution, the name of the same to be given instead of the 
street and house number. If in an industrial camp, the name of the 
camp to be given. 

(2) Full name of decedent. If an unnamed child, the surname 
preceded by ''Unnamed." 

(3) Sex.^ 

(4) Color or race, as white, black, mulatto (or other negro descent), 
Indian, Chinese, Japanese, or other. 

(5) Conjugal condition, as single, married, widowed, or divorced. 

(6) Date of birth, including the year, month, and day. 

(7) Age, in years, months, and days. If less than one day, the hours 
or minutes. 

(8) Occupation. The occupation to be reported of any person, 
male or female, who had any remunerative employment, with the state- 
ment of (a) trade, profession or particular kind of work; (6) general 
nature of industry, business, or establishment in which employed (or 
employer) . 

(9) Birthplace; at least State or foreign country, if known. 

(10) Name of father. 

(11) Birthplace of father; at least State or foreign country, if known. 

(12) Maiden name of mother. 

(13) Birthplace of mother; at least State or foreign country, if known. 

(14) Signature and address of informant. 

(15) Official signature of registrar, with the date when certificate 
was filed, and registered number. 

(16) Date of death, year, month, and day. 

(17) Certification as to medical attendance on decedent, fact and 
time of death, time last seen alive, and the cause of death, with con- 
tributory (secondary) cause of complication, if any, and duration of. 
each, and whether attributed to dangerous or insanitary conditions of 
employment; signature and address of physician or official making the 
medical certificate. 

(18) Length of residence (for inmates of hospitals and other institu- 
tions; transients or recent residents) at place of death and in the State, 
together with the place where disease was contracted, if not at place of 
death, and former or usual residence. 

(19) Place of burial or removal; date of burial. 

(20) Signature and address of undertaker or person acting as such. 



APPENDIX III 477 

The personal and statistical particulars (items 1 to 13) shall be authen- 
ticated by the signature of the informant, who may be any competent 
person acquainted with the facts. 

The statement of facts relating to the disposition of the body shall 
be signed by the undertaker or person acting as such. 

The medical certificate shall be made and signed by the physician, if 
any, last in attendance on the deceased, who s*hall specify the time in 
attendance, the time he last saw the deceased alive, and the hour of the 
day at which death occurred. And he shall further state the cause of 
death, so as to show the course of disease or sequence of causes resulting 
in the death, giving first the name of the disease causing death (primary 
cause), and the contributory (secondary) cause, if any, and the duration 
of each. Indefinite and unsatisfactory terms, denoting only symptoms 
of disease or conditions resulting from disease, will not be held sufficient 
for the issuance of a burial or removal permit ; and any certificate con- 
taining only such terms as defined by the State Registrar shall be 
returned to the physician or person making the medical certificate for 
correction and more definite statement. Causes of death which may be 
the result of either disease or violence shall be carefully defined; and if 
from violence, the means of injury shall be stated and whether (prob- 
ably) accidental, suicidal, or homicidal.^ And for deaths in hospitals, 
institutions, or of nonresidents the physician shall supply the informa- 
tion required under this head (item 18), if he is able to do so, and may 
state where, in his opinion, the disease was contracted. 

Sec. 8. That in case of any death occurring without medical attend- 
ance it shall be the duty of the undertaker to notify the local registrar 
of such death, and when so notified the registrar shall, prior to the 
issuance of the permit, inform the local health officer and refer the case 
to him for immediate investigation and certification: Provided, That 
when the local health officer is not a physician, or when there is no such 
official, and in such cases only, the registrar is authorized to make the 
certificate and return from the statement of relatives or other persons 
having adequate knowledge of the facts : Provided further, That if the 
registrar has reason to believe that the death may have been due to 
unlawful act or neglect he shall then refer the case to the coroner or 
other proper officer for his investigation and certification. And the 
coroner or other proper officer whose duty it is to hold an inquest on the 

1 In some States the question whether a death was accidental, suici- 
dal, or homicidal must be determined by the coroner or medical examiner 
and the registration law must be framed to harmonize. 



478 APPENDIX III 

body of any deceased person and to make the certificate of death 
required for a burial permit shall state in his certificate the name of the 
disease causing death, or if from external causes, (1) the means of death 
and (2) whether (probably) accidental, suicidal, or homicidal, and shall 
in any case furnish such information as may be required by the State 
Registrar in order properly to classify the death. 

Sec. 9. That the undertaker or person acting as undertaker shall file 
the certificate of death with the local registrar of the district in which 
the death occurred and obtain a burial or removal permit prior to any 
disposition of the body. He shall obtain the required personal and 
statistical particulars from the person best qualified to supply them, 
over the signature and address of his informant. He shall then present 
the certificate to the attending physician, if any, or to the health officer 
or coroner, as directed by the local registrar, for the medical certificate 
of the cause of death and other particulars necessary to complete the 
record, as specified in sections 7 and 8. And he shall then state the 
facts required relative to the date and place of burial or removal, over 
his signature and with his address, and present the completed certificate 
to the local registrar in order to obtain a permit for burial, removal, or 
other disposition of the body. The undertaker shall deliver the burial 
permit to the person in charge of the place of burial before interring or 
otherwise disposing of the body, or shall attach the removal permit to 
the box containing the corpse, when shipped by any transportation 
company, said permit to accompany the corpse to its destination, 

where, if within the State of , it shall be delivered to the person 

in charge of the place of burial. 

[Every person, firm, or corporation selling a casket shall keep a record 
showing the name of the purchaser, purchaser's post-office address, 
name of deceased, date of death, and place of death of deceased, which 
record shall be open to inspection of the State Registrar at all times. 
On the first day of each month the person, firm, or corporation selling 
caskets shall report to the State Registrar each sale for the preceding 
month, on a blank, provided for that purpose: Provided, Jiowever, That 
no person, firm, or corporation selling caskets to dealers or undertakers 
only shall be required to keep such record, nor shall such report be 
required from undertakers when they have direct charge of the disposi- 
tion of a dead body. 

Every person, firm, or corporation selling a casket at retail, and not 
having charge of the disposition of the body, shall inclose within the 
casket a notice furnished by the State Registrar calling attention to 
the requirements of the law, a blank certificate of death, and the rules 



APPENDIX III 479 

and regulations of the State board of health concerning the burial or 
other disposition of a dead body.]^ 

Sec. 10. That if the interment or other disposition of the body is to 
be made within the State, the wording of the burial or removal permit 
may be limited to a statement by the registrar, and over his signature, 
that a satisfactory certificate of death having been filed with him, as 
required by law, permission is granted to inter, remove, or dispose 
otherwise of the body, stating the name, age, sex, cause of death, and 
other necessary details upon the form prescribed by the State registrar. 

Sec. 11. That no person in charge of any premises on which inter- 
ments are made shall inter or permit the interment or other disposition 
of any body unless it is accompanied by a burial, removal, or transit 
permit, as herein provided. And such person shall indorse upon the 
permit the date of interment, over his signature, and shall return all 
permits so indorsed to the local registrar of his district within ten days 
from the date of interment, or within the time fixed by the local board 
of health. He shall keep a record of all bodies interred or otherwise 
disposed of on the premises under his charge, in each case stating the 
name of each deceased person, place of death, date of burial or disposal, 
and name and address of the undertaker; which record shall at all 
times be open to official inspection: Provided, That the undertaker, or 
person acting as such, when burying a body in a cemetery or burial 
ground having no person in charge, shall sign the burial or removal 
permit, giving the date of burial, and shall write across the face of the 
permit the words "No person in charge," and file the burial or removal 
permit within ten days with the registrar of the district in which the 
cemetery is located. 

Sec. 12. That the birth of each and every child born in this State 
shall be registered as hereinafter provided. 

Sec. 13. That within ten days after the date of each birth there shall 
be filed with the local registrar of the district in which the birth occurred 
a certificate of such birth, which certificate shall be upon the form 
adopted by the State board of health with a view to procuring a full and 
accurate report with respect to each item of information enumerated 
in section 14 of this act.^ 

In each case where a physician, midwife, or person acting as midwife 
was in attendance upon the birth, it shall be the duty of such physician, 

1 The provisions in brackets may be useful in States in which many 
funerals are conducted without regular undertakers. 

2 A proviso may be added that shall require the registration, or noti- 
fication, at a shorter interval than ten days, of births that occur in cities. 



480 APPENDIX III 

midwife, or person acting as midwife to file in accordance herewith the 
certificate herein contemplated. 

In each case where there was no physician, midwife, or person acting 
as midwife in attendance upon the birth, it shall be the duty of the father 
or mother of the child, the householder or owner of the premises where 
the birth occurred, or the manager or superintendent of the pubUc or 
private institution where the birth occurred, each in the order named, 
within ten days after the date of such birth, to report to the local 
registrar the fact of such birth. In such case and in case the physician, 
midwife, or person acting as midwife, in attendance upon the birth" is 
unable, by diligent inquiry, to obtain any item or items of information 
contemplated in section 14 of this act, it shall then be the duty of the 
local registrar to secure from the person so reporting, or from any other 
person having the required knowledge, such information as wiU enable 
him to prepare the certificate of birth herein contemplated, and it shall 
be the duty of the person reporting the birth, or who may be interro- 
gated in relation thereto, to answer correctly and to the best of his 
knowledge all questions put to him by the local registrar which may be 
calculated to elicit any information needed to make a complete record 
of the birth as contemplated by said section 14, and it shall be the duty 
of the informant as to any statement made in accordance herewith to 
verify such statement by his signature, when requested so to do by the 
local registrar. 

Sec. 14. That the certificate of birth shall contain the following 
items, which are hereby declared necessary for the legal, social, and 
sanitary purposes subserved by registration records i^ 

(1) Place of birth, including State, county, township or town, village, 
or city. If in a city, the ward, street, and house number; if in a hospi- 
tal or other institution, the name of the same to be given, instead of the 
street and house number. 

(2) Full name of child. If the child dies without a name, before the 
certificate is filed, enter the words "Died unnamed." If the living child 
has not yet been named at the date of filing certificate of birth, the space 
for "Full name of child" is to be left blank, to be filled out subsequently 
by a supplemental report, as hereinafter provided. 

(3) Sex of child. 

(4) Whether a twin, triplet, or other plural birth. A separate 
certificate shall be required for each child in case of plural births. 

^ The following items are those of the United States standard certi- 
ficate of birth, approved by the Bureau of the Census. 



APPENDIX III 481 

(5) For plural births, number of each child in order of birth. 

(6) Whether legitimate or illegitimate. ^ 

(7) Date of birth, including the year, month, and day. 

(8) Full name of father. 

(9) Residence of father. 

(10) Color or race of father. 

(11) Age of father at last birthday, in years. 

(12) Birthplace of father; at least State or foreign country, if known. 

(13) Occupation of father. The occupation to be reported if engaged 
in any remunerative employment, with the statement of (a) trade, 
profession, or particular kind of work; (6) general nature of industry, 
business, or establishment in which employed (or employer). 

(14) Maiden name of mother. 

(15) Residence of mother. 

(16) Color or race of mother. 

(17) Age of mother at last birthday, in years. 

(18) Birthplace of mother; at least State or foreign country, if 
known. 

(19) Occupation of mother. The occupation to be reported if 
engaged in any remunerative employment, with the statement of (a) 
trade, profession, or particular kind of work; (b) general nature of 
industry, business, or establishment in which employed (or employer). 

(20) Number of children born to this mother, including present birth. 

(21) Number of children of this mother living. 

(22) The certification of attending physician or midwife as to attend- 
ance at birth, including statement of year, month, day (as given in item 
7), and hour of birth, and whether the child was born alive or stillborn. 
This certification shall be signed by the attending physician or midwife, 
with date of signature and address; if there is not physician or midwife 
in attendance, then by the father or mother of the child, householder, 
owner of the premises, or manager or superintendent of public or private 
institution where the birth occurred, or other competent person, whose 
duty it shall be to notify the local registrar of such birth, as required by 
section 13 of this act. 

(23) Exact date of filing in office of local registrar, attested by his 
official signature, and registered number of birth, as hereinafter pro- 
vided. 

Sec. 15. That when any certificate of birth of a living child is pre- 
sented without the statement of the given name, then the local registrar 

^ This question may be omitted if desired, or provision may be made 
so that the identity of parents will not be disclosed. 



482 • APPENDIX III 

shall make out and deliver to the parents of the child a special blank for 
the supplemental report of the given name of the child, which shall be 
filled out as directed, and returned to the local registrar as soon as the 
child shall have been named. 

Sec. 16. That every physician, midwife, and undertaker shall, with- 
out delay, register his or her name, address, and occupation with the 
local registrar of the district in which he or she resides, or may hereafter 
establish a residence; and shall thereupon be supplied by the local 
registrar with a copy of this act, together with such rules and regulations 
as may be prepared by the State registrar relative to its enforcement. 
Within thirty days after the close of each calendar year each local 
registrar shall make a return to the State registrar of all physicians, 
midwives, or undertakers who have been registered in his district 
during the whole or any part of the preceding calendar year : Provided. 
That no fee or other compensation shall be charged by local registrars 
to physicians, midwives, or undertakers for registering their names 
under this section or making returns thereof to the State registrar.^ 

Sec. 17. That all superintendents or managers, or other persons in 
charge of hospitals, almshouses, lying-in, or other institutions, public 
or private, to which persons resort for treatment of diseases, confinement, 
or are committed by process of law, shall make a record of all the per- 
sonal and statistical particulars relative to the inmates in their institu- 
tions at the date of approval of this act, which are required in the forms 
of the certificates provided for by this act, as directed by the State 
registrar; and thereafter such record shall be, by them, made for all 
future inmates at the time of their admittance. And in case of persons 
admitted or committed for treatment of disease, the physician in charge 
shall specify for entry in the record, the nature of the disease, and 
where, in his opinion, it was contracted. The personal particulars and 
information required by this section shall be obtained from the indi- 
• vidual himself if it is practicable to do so; and when they can not be so 
obtained, they shall be obtained in as complete a manner as possible 
from relatives, friends, or other persons acquainted with the facts. 

Sec. 18. That the State registrar shall prepare, print, and supply to 
all registrars all blanks and forms used in registering, recording, and 
preserving the returns, or in otherwise carrying out the purposes of this 
act; and shall prepare and issue such detailed instructions as may be 
required to procure the uniform observance of its provisions and the 

1 This section may be omitted if deemed expedient and the duty of 
supplying instructions may be assumed by the State officer. 



APPENDIX III 483 

maintenance of a perfect system of registration; and no other blanks 
shall be used than those supplied by the State registrar. He shall care- 
fully examine the certificates received monthly from the local registrars, 
and if any such are incomplete or unsatisfactory he shall require such 
further information to be supplied as may be necessary to make the 
record complete and satisfactory. And all physicians, midwives, 
informants, or undertakers, and all other persons having knowledge of 
the facts, are hereby required to supply, upon a form provided by the 
State registrar or upon the original certificate, such information as they 
may possess regarding any birth or death upon demand of the State 
registrar, in person, by mail, or through the local registrar: Provided, 
That no certificate of birth or death, after its acceptance for registration 
by the local registrar, and no other record made in pursuance of this act, 
shall be altered or changed in any respect otherwise than by amendments 
properly dated, signed, and witnessed. The State registrar shall 
further arrange, bind, and permanently preserve the certificates in a 
systematic manner, and shall prepare and maintain a comprehensive 
and continuous card index of all births and deaths registered; said 
index to be arranged alphabetically, in the case of deaths, by the names 
of decendents, and in the case of births, by the names of fathers and 
mothers. He shall inform all registrars what diseases are to be con- 
sidered infectious, contagious, or communicable and dangerous to the 
public ^health, as decided by the State board of health, in order that 
when deaths occur from such diseases proper precautions may be taken 
to prevent their spread. 

If any cemetery company or association, or any church or historical 
society or association, or any other company, society, or association, 
or any individual, is in possession of any record of births or deaths 
which may be of value in establishing the genealogy of any resident of 
this State, such company, society, association, or individual may file 
such record or a duly authenticated transcript thereof with the State 
registrar, and it shall be the duty of the State registrar to preserve such 
record or transcript and to make a record and index thereof in such form 
as to facilitate the finding of any information contained therein. Such 
record and index shall be open to inspection by the public, subject to 
such reasonable conditions as the State registrar may prescribe. If 
any person desires a transcript of any record filed in accordance here- 
with, the State registrar shall furnish the same upon application, to- 
gether with a certificate that it is a true copy of such record, as filed in 
his office, and for his services in so furnishing such transcript and 
certificate he shall be entitled to a fee of (ten cents per folio) (fifty cents 



484 APPENDIX III ■ 

per hour or fraction of an hour necessarily consumed in making such 
transcript) and to a fee of twenty-five cents for the certificate, which 
fees shall be paid by the applicant. 

Sec. 19. That each local registrar shall supply blank forms of certi- 
ficates to such persons as require them. Each local registrar shall 
carefully examine each certificate of birth or death when presented for 
record in order to ascertain whether or not it has been made out in 
accordance with the provisions of this act and the instructions of the 
State registrar; and if any certificate of death is incomplete or unsatis- 
factory, it shall be his duty to call attention to the defects in the return, 
and to withhold the burial or removal permit until such defects are 
corrected. All certificates, either of birth or of death, shall be written 
legibly, in durable black ink, and no certificate shall be held to be com- 
plete and correct that does not supply all of the items of information 
called for therein, or satisfactorily account for their omission. If the 
certificate of death is properly executed and complete, he shaU then 
issue a burial or removal permit to the undertaker; provided, t\m,t in 
case the death occurred from some disease which is held by the State 
board of health to be infectious, contagious, or communicable and 
dangerous to the public health, no permit for the removal or other dis- 
position of the body shall be issued by the registrar, except under such 
conditions as may be prescribed by the State board of health. If a 
certificate of birth is incomplete, the local registrar shall immediately 
notify the informant and require him to supply the missing items of 
information if they can be obtained. He shall number consecutively 
the certificates of birth and death, in two separate series, beginning 
with number 1 for the first birth and the first death in each calendar 
year, and sign his name as registrar in attest of the date of filing in his 
office. He shall also make a complete and acciu^ate copy of each birth 
and each death certificate registered by him in a record book suppHed 
by the State registrar, to be preserved permanently in his office as the 
local record, in such manner as directed by the State registrar. And 
he shall, on the tenth day of each month, transmit to the State registrar 
all original certificates registered by him for the preceding month. And 
if no births or no deaths occurred in any month, he shall, on the tenth 
day of the following month, report that fact to the State registrar, on a 
card provided for such purpose. 

Sec. 20. That each local registrar shall be paid the sum of twenty-five 
cents for each birth certificate and each death certificate properly and 
completely made out and registered with him, and correctly recorded 
and promptly returned by him to the State registrar, as required by 



APPENDIX III 485 

this act.^ And in case no births or no deaths were registered during 
any month, the local registrar shall be entitled to be paid the sum of 
twenty-five cents for each report to that effect, but only if such report 
be made promptly as required by this act. All amounts payable to a 
local registrar under the provisions of this section shall be paid by the 
treasurer of the county in which the registration district is located, upon 
certification by the State registrar. And the State registrar shall 
annually certify to the treasurers of the several counties the number of 
births and deaths properly registered, with the names of the local 
registrars and the amounts due each at the rates fixed herein .^ 

Sec. 21. That the State registrar shall, upon request, supply to any 
applicant a certified copy of the record of any birth or death registered 
under provisions of this act, for the making and certification of which 
he shall be entitled to a fee of fifty cents, to be paid by the applicant. 
And any such copy of the record of a birth or death, when properly 
certified by the State registrar, shall be prima facie evidence in all 
courts and places of the facts therein stated. For any search of the 
files and records when no certified copy is made, the State registrar 
shall be entitled to a fee of fifty cents for each hour or fractional part of 
an hour of time of search, said fee to be paid by the applicant. And the 
State registrar shall keep a true and correct account of all fees by him 
received under these provisions, and turn the same over to the State 
treasurer : Provided^ That the State registrar shall, upon request of any 
parent or guardian, supply, without fee, a certificate limited to a state- 
ment as to the date of birth of any child when the same shall be neces- 
sary for admission to school, or for the purpose of securing employment : 
And -provided further , That the United States Census Bureau may obtain, 
without expense to the State, transcripts, or certified copies of births 
and deaths without payment of the fees herein prescribed. 

Sec. 22. That any person, who for himself or as an officer, agent, or 
employee of any other person, or of any corporation or partnership (a) 
shall inter, cremate, or otherwise finally dispose of the dead body of a 
human being, or permit the same to be done, or shall remove said body 
from the primary registration district in which the death occurred or 

^ A proviso may be inserted at this point relative to fees of city 
registrars who are already compensated by salary for their services. 
See laws of Missouri, Ohio, and Pennsylvania. 

2 Provision may be made in this section for the payment of sub- 
registrars and also, if desired, for the payment of physicians and mid- 
wives. See Kentucky law. 



486 APPENDIX III 

the body was found without the authority of a burial or removal permit 
issued by the local registrar of the district in which the death occurred 
or in which the body was found; or (h) shall refuse or fail to furnish 
correctly any information in his possession, or shall furnish false in- 
formation affecting any certificate or record, required by this act; or 
(c) shall willfully alter, otherwise than is provided by section 18 of this 
act, or shall falsify any certificate of birth or death, or any record 
established by this act; or {d) being required by this act to fill out a 
certificate of birth or death and file the same with the local registrar, 
or deliver it, upon request, to any person charged with the duty of filling 
the same, shall fail, neglect, or refuse to perform such duty in the 
manner required by this act; or (e) being a local registrar, deputy 
registrar, or subregistrar, shall fail, neglect, or refuse to perform his 
duty as required by this act and by the instructions and direction of the 
State registrar thereunder, shall be deemed guilty of a misdemeanor, 
and upon conviction thereof shall for the first offense be fined not less 
than five dollars ($5) nor more than fifty. dollars ($50), and for each 
subsequent offense not less than ten dollars ($10) nor more than one 
hundred doUard ($100), or be imprisoned in the county jail not more than 
sixty days, or be both fined and imprisoned in the discretion of the 
court .^ 

Sec. 23. That each local registrar is hereby charged with the strict 
and thorough enforcement of the provisions of this act in his registration 
district, under the supervision and direction of the State registrar. 
And he shall make an immediate report to the State registrar of any 
violation of this law coming to his knowledge, by observation or upon 
complaint of any person or otherwise. 

The State registrar is hereby charged with the thorough and efficient 
execution of the provisions of this act in every part of the State, and is 
hereby granted supervisory power over local registrars, deputy local 
registrars, and subregistrars to the end that all of its requirements shall 
be uniformly complied with. The State registrar, either personally op 
by an accredited representative, shall have authority to investigate 
cases of irregularity or violation of law, and all registrars shall aid him 
upon request, in such investigations. When he shall deem it necessary 
he shall report cases of violation of any of the provisions of this act to 
the prosecuting attorney of the county, with a statement of the facts 

^ Provision may be made whereby compliance with this act shall 
constitute a condition of granting licenses to physicians, midwives, and 
embalmers. 



APPENDIX III 487 

and circumstances; and when any such case is reported to him by the 
State registrar the prosecuting attorney shall forthwith initiate and 
promptly follow up the necessary court proceedings against the person 
or corporation responsible for the alleged violation of law. And upon 
request of the State registrar, the attorney general shall assist in the 
enforcement of the provisions of this act. 

Note. — Other sections should be added giving the date on which 
the act is to go into effect, if not determined by constitutional provisions 
of the State; providing for the financial support of the law; and repeal- 
ing prior statutes inconsistent with the present act. 

It is desirable that the entire bill should be reviewed by competent 
legal authority for the purpose of discovering whether it can be made 
more consistent in any respect with the general form of legislation of. 
the State in which the bill is to be introduced, without material change 
or injury to the effectiveness of registration. 

THE STANDARD BIRTH AND DEATH CERTIFICATES 

The following are facsimile reproductions of the standard birth and 
death certificates. They have been reduced in size to meet the require- 
ments of the printed page. The size of the birth certificate is 6| by 
7| inches, and of the death certificate 7j by 8| inches. Copies can be 
obtained from the Director of the Census upon request. 



488 



APPENDIX III 



UNITED STATES STANDARD CERTIFICATE OF BIRTH 



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PLACE OF BIRTH department of commerce and labor 

BUREAU OF THE CENSUS 

County of STANDARD CERTIFICATE OF BIRTH 



Registered No. 



Township of 

or 
Village of 

or 
City of (No St.; Ward) 

f If child is not yet named, make 
\supplemental report as directed 



FULL NAME OF CHILD. 



Sex of 
Child 



Twin, triplet, I Number in order 
or other? | of birth 

(To be answered only in event of plural births; 



Legiti- 
mate? 



Date of birth 
, 19.. 

(Month) (Day) (Year) 



FATHER 



FULL 

NAME 



RESIDENCE 



AGE AT LAST 
BIRTHDAY . . 



(Tears) 



BIRTHPLACE 



OCCUPATION 



Number of children born to this 
mother, including present birth. . . 



FULL 

MAIDEN 

NAME 



RESIDENCE 



AGE AT LAST 
BIRTHDAY . 



(Years) 



BIRTHPLACE 



OCCUPATION 



Number of children of this mother 
now living 



CERTIFICATE OF ATTENDING PHYSICIAN OR MIDWIFE 1 

I hereby certify that I attended the birth of this child, who was 
at M., on the date above stated. 

(Born alive or Stillborn) 



(Signature) . 



■ 1 When there was no attending physician 
or midwife, then the father, householder, 
etc., should make this return. A stillborn 
child is one that neither breathes nor shows 
other evidence of life after birth. 

Given name added from a supplemental Address 

report , 19 

Filed ,19 

. . 11-385 H 

BegiBtrar 



(Physician or Midwife) 



Regiatrar 



APPENDIX III 



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SUPPLEMENTAL REPORT OF BIRTH 

(state) 
(This return should preferably be made by the person who made the original ) 

Registered Number i 

Place of birth i No St. 

(Registration district) 

' I HEREBY CERTIFY that the 



SEX of 
CHILD 1 



Twin.i 1 jNumbei 
triplet, J-and<in order 
or other? J lot birth 



DATE OF BIRTH 1 190 . . 

(Month) (Day) (Year) 



FULL 1 
NAME 



FULL 1 
MAIDEN 

NAME 



child described herein 
has been named: 



(Gire name in full) 



(Snrname) 



(Signature) . 



1 These items to be entered by the 
Registrar before giving out this form. 



(Phyticiftn or midwife) 



490 



APPENDIX III 



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PERSONAL AND STATISTICAL PARTICULARS 



DEPARTMENT OP COMMERCE 
BUREAU OF THE CENSUS 

STANDARD CERTIFICATE OF DEATH 

1 PLACE OF DEATH 

County. State Registered No 

Township or Village or 

City No .St.,. . . . . .Ward 

(If death occurred in a hospital or institution, 
give its NAME instead of street and number.) 



a FULL NAME 

(a) Residence. No St., Ward 

■ (Usual place of abode.) (If nonresident give city or town and State.) 

Length of residence in city or town How long in U. S., if of for- 

where death occurred, yrs. mos. ds. eign birth? yrs. mos. ds. 



3 SEX 



4 COLOR 
OR RACE 



5 Single, Married, 
Widowed, or 
Divorced 

(Write the word) 



5* If married, widowed, or divorced 

HUSBAND of 

(or) WIFE of 



6 DATE OF BIRTH (month, day, and 
year) 



7 AGE Yrs. 



Mos. 



Ds. 



If LESS than 
1 day, . . . hrs. 
or min.? 



8 OCCUPATION OF DECEASED 

(a) Trade, profession, or 
particular kind of work 

(b) General nature of industry, 
business, or establishment in 
which employed (or employer) . . . , 

(c) Name of employer 



9 BIRTHPLACE (city or town) . 
(State or country) 



10 NAME OF FATHER 



11 BIRTHPLACE OF FATHER (city Or 

town) 

(State or country) 



12 MAIDEN NAME -OF MOTHER 



13 BIRTHPLACE OF MOTHER (city Or 

town) 

(State or country) 



1* Informant . 
(Address) 



15 Filed 19 



Registrar 



MEDICAL CERTIFICATE OF DEATH 



16 DATE OF DEATH (month, day, and 
year) 19 



' I HEREBY CERTIFY, That 
I attended deceased from 

, 19 to , 19,. 

that I last saw h... alive on 19.. 

and that death occurred, on the 

date stated above, at m. 

The CAUSE OF DEATH* was as follows: 



(duration) . . .jnrs. . . . mos. . . ds. 

CONTRIBUTORY 

(Secondary) 

(duration) . . .yrs. . . mos. . . ds. 

18 Where was disease contracted 
if not at place of death? 

Did an operation precede death? 

• Date of 

Was there an autopsy? 

What test confirmed diagnosis? 

(Signed) , M.D. 

, 19 (Address) 



* State the Disease Causing Death, 
or in deaths from Violent Causes, 
state (1) Means and Nature of In- 
jury; and (2) whether Accidental, 
Suicidal , or Homicidal . (See reverse 
side for additional space.) 



19 PLACE OF BURIAL, 
CREMATION, OR RE- 
MOVAL 



20 UNDERTAKER 



DATE OF BURLVL 



19 



APPENDIX IV. 

TABLE VI.— LOGARITHMS OF NUMBERS. 



N 


0123466789 


100 


00000 00043 00087 00130 00173 00217 00260 00303 00346 00389 


1 


0432 0475 0518 0561 0604 0647 0689 0732 0775 0817 


2 


0860 0903 0945 0988 1030 1072 1115 1157 1199 1242 


3 


1284 1326 1368 1410 1452 1494 1536 1578 1620 1662 


4 


1703 1745 1787 1828 1870 1912 1953 1995 2036 2078 


5 


2119 2160 2202 2243 2284 2325 2366 2407 2449 2490 


6 


2531 2572 2612 2653 2694 2735 2776 2816 2857 2898 


7 


2938 2979 3019 3060 3100 3141 3181 3222 3262 3302 


8 


3342 3383 3423 3463 3503 3543 3583 3623 3663 3703 


9 


3743 3782 3822 3862 3902 3941 3981 4021 4060 4100 


110 


04139 04179 04218 04258 04297 04336 04376 04415 04454 04493 


1 


4532 4571 4610 4650 4689 4727 4766 4805 4844 4883 


2 


4922 4961 4999 5038 5077 5115 5154 5192 5231 5269 


3 


6308 5346 5385 5423 5461 5500 5538 5576 5614 5652 


4 


6690 6729 6767 5805 5843 5881 5918 5956 5994 6032 


6 


6070 6108 6145 6183 6221 6258 6296 6333 6371 6408 


6 


6446 6483 6521 6558 6595 6633 6670 6707 6744 6781 


7 


6819 6856 6893 6930 6967 7004 7041 7078 7115 7151 


8 


7188 7225 7262 7298 7335 7372 7408 7445 7482 7518 


9 


7665 7591 7628 7664 7700 7737 7773 7809 7846 7882 


120 


07918 07954 07990 08027 08063 08099 08135 08171 08207 08243 


1 


8279 8314 8350 8386 8422 8458 8493 8529 8565 8600 


2 


8636 8672 8707 8743 8778 8814 8849 8884 8920 8956 


3 


8991 9026 9061 9096 9132 9167 9202 9237 9272 9307 


4 


9342 9377 9412 9447 9482 9517 9552 9587 9621 9666 


5 


9691 9726 9760 9795 9830 9864 9899 9934 9968 10003 


6 


10037 10072 10106 10140 10175 10209 10243 10278 10312 0346 


7 


0380 0415 0449 0483 0517 0551 0585 0619 0653 0687 


8 


0721 0755 0789 0823 0857 0890 0924 0958 0992 1026 


9 


1059 1093 1126 1160 1193 1227 1261 1294 1327 1361 


130 


11394 11428 11461 11494 11528 11561 11594 11628 11661 11694 


1 


1727 1760 1793 1826 1860 1893 1926 1959 1992 2024 


2 


2067 2090 2123 2156 2189 2222 2254 2287 2320 2352 


3 


2386 2418 2460 2483 2516 2648 2681 2613 2646 2678 


4 


2710 2743 2775 2808 2840 2872 2905 2937 2969 3001 


6 


3033 3066 3098 3130 3162 3194 3226 3258 3290 3322 


6 


3364 3386 3418 3450 3481 3513 3546 3677 3609 3640 


7 


3672 3704 3735 3767 3799 3830 3862 3893 3925 3956 


8 


3988 4019 4051 4082 4114 4145 4176 4208 4239 4270 


9 


4301 4333 4364 4395 4426 4457 4489 4520 4651 4682 


140 


14613 14644 14675 14706 14737 14768 14799 14829 14860 14891 


1 


4922 4953 4983 5014 5045 6076 6106 5137 6168 5198 


2 


6229 6259 5290 6320 6351 5381 6412 6442 6473 6603 


3 


6534 6564 5594 5625 6655 5685 5715 5746 5776 6806 


4 


5836 5866 6897 5927 6957 5987 6017 6047 6077 6107 


5 


6137 6167 6197 6227 6256 6286 6316 6346 6376 0406 


6 


6435 6465 6495 6524 6554 6684 6613 6643 6673 6702 


7 


6732 6761 6791 6820 6850 6879 6909 6938 6967 6997 


8 


7026 7056 7085 7114 7143 7173 7202 7231 7260 7289 


9 


7319 7348 7377 7406 7435 7464 7493 7522 7551 7580 


150 


17609 17638 17667 17696 17726 17764 17782 17811 17840 17869 

1 



491 



492 TABLE VI.— LOGARITHMS OF NUMBERS. 



150 


O 12 34567 89 


17609 17638 17667 17696 17725 17754 17782 17811 17840 17869 


1 


7898 7926 7955 7984 8013 8041 8070 8099 8127 8156 


2 


8184 8213 8241 8270 8298 8327 8355 8384 8412 8441 


3 


8469 8498 8526 8554 8583 8611 8639 8667 8696 8724 


4 


8752 8780 8808 8837 8865 8893 8921 8949 8977 9005 


5 


9033 9061 9089 9117 9145 9173 9201 9229 9257 9285 


6 


9312 9340 9368 9396 9424 9451 9479 9507 9535 9562 


1 


9590 9618 9645 9673 9700" 9728 9756 9783 9811 9838 


8 


9866 9893 9921 9948- 9976 20003 20030 20058 20085 20112 


9 


20140 20167 20194 20222 20249 0276 0303 0330 0358 0385 


160 


20412 20439 20466 20493 20520 20548 20575 20602 20629 20656 


1 


0683 0710 0737 0763 0790 0817 0844 0871 0898 0925 


2 


0952 0978 1005 1032 1059 1085 1112 1139 1165 1192 


3 


1219 1245 1272 1299 1325 1352 1378 1405 1431 1458 


4 


1484 1511 1537 1564 1590 1617 1643 1669 1696 1722 


5 


1748 1775 1801 1827 1854 1880 1906 1932 1958 1985 


6 


2011 2037 2063 2089 2115 2141 2167 2194 2220 2246 


7 


2272 2298 2324 2350 2376 2401 2427 2453 2479 2505 


8 


2531 2557 2583 2608 2634 2660 2686 2712 2737 2763 


9 


2789 2814 2840 2866 2891 2917 2943 2968 2994 3019 


170 


23045 23070 23096 23121 23147 23172 23198 23223 23249 23274 


1 


3300 3325 3350 3376 3401 3426 3452 3477 3502 3528 


2 


3553 3578 3603 3629 3654 3679 3704 3729 3754 3779 


3 


3805 3830 3855 3880 3905 3930 3955 3980 4005 4030 


4 


4055 4080 4105 4130 4155 4180 4204 4229 4254 4279 


5 


4304 4329 4353 4378 4403 4428 4452 4477 4502 4527 


6 


4551 4576 4601 4625 4650 4674 4699 4724 4748 4773 


7 


4797 4822 4846 4871 4895 4920 4944 4969 4993 5018 


8 


5042 5066 5091 6115 6139 6164 6188 6212 6237 6261 


9 


6285 6310 6334 6368 6382 6406 6431 6455 6479 5503 


180 


25627 26561 25575 25600 25624 25648 25672 25696 25720 25744 


1 


6768 5792 6816 6840 6864 6888 5912 5935 5959 5983 


2 


6007 6031 6065,6079 6102 6126 6160 6174 6198 6221 


3 


6245 6269 6293 6316 6340 6364 6387 6411 6435 6458 


4 


6482 6505 6529 6653 6576 6600 6623 6647 6670 6694 


5 


6717 6741 6764 6788 6811 6834 6858 6881 6905 6928 


6 


6951 6975 6998 7021 7045 7068 7091 7114 7138 7161 


7 


7184 7207 7231 7254 7277 7300 7323 7346 7370 7393 


8 


7416 7439 7462 7485 7508 7631 7554 7677 7600 7623 


9 


7646 7669 7692 7715 7738- 7761 7784 7807 7830 7862 


190 


27875 27898 27921 27944 27967 27989 28012 28035 28058 28081 


1 


8103 8126 8149 8171 8194 8217 8240 8262 8285 8307 


2 


8330 8353 8375 8398 8421 8443 8466 8488 8511 8533 


3 


8556 8578 8601 8623 8646 8668 8691 8713 8735 8758 


4 


8780 8803 8825 8847 8870 8892 8914 8937 8959 8981 


5 


9003 9026 9048 9070 9092 9115 9137 9159 9181 . 9203 


• 6 


9226 9248 9270 9292 9314 9336 9358 9380 9403 9425 


7 


9447 9469 9491 9513 9535 9557 9579 9601 9623 9645 


8 


9667 9688 9710 9732 9754 9776 9798 9820 9842 9863 


9 


9885 9907 9929 9951 9973 9994 30016 30038 30060 30081 


200 


30103 30125 30146 30168 30190 30211 30233 30255 30276 30298 

- 





TABLE VI.— LOaARITHMS OP NUMBERS. 493 


N 


012345.6 789 


200 


30103 30125 30146 30168 30190 30211 30233 30255 30276 30298 


1 


0320 0341 0363 0384 0406 0428 0449 0471 0492 0514 


2 


0535 0557 0578 0600 0621 0643 0664 0685 0707 0728 


3 


0750 0771 0792 0814 0835 0856 0878 0899 0920 0942 


4 


0963 0984 1006 1027 1048 1069 1091 1112 1133 1154 


5 


1175 1197 1218 1239 1260 1281 1302 1323 1345 1366 


6 


1387 1408 1429 1450 1471 1492 1513 1534 1555 1576 


7 


1597 1618 1639 1660 1681 1702 1723 1744 1765 1785 


8 


1806 1827 1848 1869 1890 1911 1931 1952 1973 1994 


9 


2015 2035 2056 2077 2098 2118 2139 2160 2181 2201 


210 


32222 32243 32263 32284 32305 32325 32346 32366 32387 32408 


1 


2428 2449 2469 2490 2510 2531 2552 2572 2593 2613 


2 


2634 2654 2675 2695 2715 2736 2756 2777 2797 2818 


3 


2838 2858 2879 2899 2919 2940 2960 2980 3001 3021 


4 


3041 3062 3082 3102 3122 3143 3163 3183 3203 3224 


5 


3244 3264 3284 3304 3325 3345 3365 3385 3405 3425 


6 


3445 3465 3486 3506 3526 3546 3566 3586 3606 3626 


7 


3646 3666 3686 3706 3726 3746 3766 3786 3806 3826 


8 


3846 3866 3885 3905 3925 3945 3965 3985 4005 4025 


9 


4044 4064 4084 4104 4124 4143 4163 4183 4203 4223 


220 


34242 34262 34282 34301 34321 34341 34361 34380 34400 34420 


1 


4439 4459 4479 4498 4518 4537 4557 4577 4596 4616 


2 


4635 4655 4674 4694 4713 4733 4753 4772 4792 4811 


3 


4830 4850 4869 4889 4908 4928 4947 4967 4986 5005 


4 


5025 5044 5064 5083 5102 6122 5141 5160 5180 5199 


5 


5218 5238 5257 5276 5295 5315 5334 5353 5372 5392 


6 


5411 5430 5449 5468 5488 6507 6526 5545 6564 5583 


7 


6603 6622 5641 5660 5679 6698 6717 5736 6755 5774 


8 


6793 6813 6832 5851 6870 6889 6908 6927 6946 6965 


9 


6984 6003 6021 6040 6059 6078 6097 6116 6135 6154 


280 


36173 36192 36211 36229 36248 36267 36286 36305 36324 36342 


1 


6361 6380 6399 6418 6436 6455 6474 6493 6511 6630 


2 


6549 6568 6586 6605 6624 6642 6661 6680 6698 6717 


3 


6736 6754 6773 6791 6810 6829 6847 6866 6884 6903 


4 


6922 6940 6959 6977 6996 7014 7033 7051 7070 7088 


5 


7107 7125 7144 7162 7181 7199 7218 7236 7254 7273 


6 


7291 7310 7328 7346 7365 7383 7401 7420 7438 7457 


7 


7475 7493 7511 7530 7548 7566 7585 7603 7621 7639 


8 


7658 7676 7694 7712 7731 7749 7767 7785 7803 7822 


9 


7840 7858 7876 7894 7912 7931 7949 7967 7985 8003 


240 


38021 38039 38057 38075 38093 38112 38130 38148 38166 38184 


1 


8202 8220 8238 8256 8274 8292 8310 8328 8346 8364 


2 


8382 8399 8417 8435 8453 8471 8489 8507 8525 8543 


3 


8561 8578 8596 8614 8632 8650 8668 8686 8703 8721 


4 


8739 8757 8775 8792 8810 8828 8846 8863 8881 8899 


5 


8917 8934 8952 8970 8987 9005 9023 9041 9058 9076 


6 


9094 9111 9129 9146 9164 9182 9199 9217 9235 9252 


7 


9270 9287 9305 9322 9340 9358 9375 9393 9410 9428 


8 


9445 9463 9480 9498 9515 9533 9550 9568 9585 9602 


9 


9620 9637 9655 9672 9690 9707 9724 9742 9769 9777 


250 


39794 39811 39829 39846 39863 39881 39898 39915 39933 39960 



494 TABLE VI.— LOGARITHMS OF NUMBERS. 



N 

250 

1 
2 
3 

4 
5 
6 
7 
8 
9 

260 

1 
2 
3 

4 
5 
6 
7 
8 
9 

270 

1 
2 
3 
4 
5 
6 
7 
8 
9 

280 
1 
2 
3 
4 
5 
6 
7 
8 
9 

290 

1 
2 
3 

4 
5 
6 
7 
8 
9 

300 



0123456789 



39794 39811 39829 39846 39863 39881 39898 39915 39933 39950 

9967 9985 40002 40019 40037 40054 40071 40088 40106 40123 

40140 40157 0175 0192 0209 0226 0243 0261 0278 0295 

0312 0329 0346 0364 0381 0398 0415 0432 0449 0466 

0483 0500 0518 0535 0552 0569 0586 0603 0620 0637 

0654 0671 0688 0705 0722 0739 0756 0773 0790 0807 

0824 0841 0858 0875 0892 0909 0926 0943 0960 0976 

0993 1010 1027 1044 1061 1078 1095 1111 1128 1145 

1162 1179 1196 1212 1229 1246 1263 1280 1296 1313 

1330 1347 1363 1380 1397 1414 1430 1447 1464 1481 

41497 41514 41531 41547 41564 41581 41597 41614 41631 41647 

1664 1681 1697 1714 1731 1747 1764 1780 1797 1814 

1830 1847 1863 1880 1896 1913 1929 1946 1963 1979 

1996 2012 2029 2015 2062 2078 2095 2111 2127 2144 

2160 2177 2193 2210 2226 2243 2259 2275 2292 2308 

2325 2341 2357 2374 2390 2406 2423 2439 2455 2472 

2488 2504 2521 2537 2553 2570 2586 2602 2619 2635 

2651 2667 2684 2700 2716 2732 2749 2765 2781 2797 

2813 2830 2846 2862 2878 2894 2911 2927 2943 2959 

2975 2991 3008 3024 3040 3056 3072 3088 3104 3120 

43136 43152 43169 43185 43201 43217 43233 43249 43265 43281 

3297 3313 3329 3345 3361 3377 3393 3409 3425 3441 

3457 3473 3489 3505 3521 3537 3553 3569 3584 3600 

3616 3632 3648 3664 3680 3696 3712 3727 3743 3759 

3775 3791 3807 3823 3838 3854 3870 3886 3902 3917 

3933 3949 3965 3981 3996 4012 4028 4044 4059 4075 

4091 4107 4122 4138 4154 4170 4185 4201 4217 4232 

4248 4264 4279 4295 4311 4326 4342 4358 4373 4389 

4404 4420 4436 4451 4467 4483 4498 4514 4529 4545 

4560 4576 4592 4607 4623 4638 4654 4669 4685 4700 

44716 44731 44747 44762 44778 44793 44809 44824 44840 44855 

4871 4886 4902 4917 4932 4948 4963 4979 4994 5010 

5025 5040 5056 5071 5086 5102 <6117 5133 5148 5163 

5179 5194 5209 5225 5240 5255 5271 6286 5301 5317 

5332 5347 5362 5378 5393 5408 5423 5439 5454 5469 

5484 6500 6515 5530 5545 5561 5576 6591 5606 5621 

5637 6662 5667 5682 6697 6712 6728 6743 6758 5773 

5788 5803 5818 5834 5849 6864 5879 5894 5909 5924 

5939 6954 5969 6984 6000 6015 6030 6045 6060 6075 

6090 6105 6120 6135 6150 6165 6180 6195 6210 6225 

46240 46255 46270 46285 46300 46315 46330 46345 46359 46374 

6389 6404 6419 6434 6449 6464' 6479 6494 6509 6523 

6538 6553 6568 6583 6598 6613 6627 6642 6657 6672 

6687 6702 6716 6731 6746 • 6761 6776 6790 6806 6820 

6835 6850 6864 6879 6894 6909 6923 6938 6953. 6967 

6982 6997 7012 7026 7041 7066 7070 7086 7100 7114 

7129 7144 7159 7173 7188 7202 7217 7232 7246 7261 

7276 7290 7305 7319 7334 7349 7363 7378 7392 7407 

7422 7436 7451 7465 7480 7494 7609 7624 7638 7653 

7567 7582 7596 7611 7625 7640 7654 7669 7683 7698 

47712 47727 47741 47766 47770 47784 47799 47813 47828 47842 



TABLE VI.— LOGARITHMS OF NUMBERS. ' 495 



N 0123456789 



300 

1 
2 
3 
4 
5 
6 
7 
8 
9 

810 

1 
2 
3 
4 
5 
6 
7 
8 
9 

320 

1 
2 
3 
4 
5 
6 
7 
8 
9 

330 

1 
2 
3 
4 
5 
6 
7 
8 
9 

340 

1 
2 
3 
4 
5 
6 
7 
8 
9 

350 



47712 47727 47741 47756 47770 47784 47799 47813 47828 47842 

7857 7871 7885 7900 7914 7929 7943 7958 7972 7986 

8001 8015 8029 8044 8058 8073 8087 8101 8116 8130 

8144 8159 8173 8187 8202 8216 8230 8244 8259 8273 

8287 8302 8316 8330 8344 8359 8373 8387 8401 8416 

8430 8444 8458 8473 8487 8501 8515 8530 8544 8558 

8572 8586 8601 8615 8629 8643 8657 8671 8686 8700 

8714 8728 8742 8756 8770 8785 8799 8813 8827 8841 

8855 8869 8883 8897 8911 8926 8940 8954 8968 8982 

8996 9010 9024 9038 9052 9066 9080 9094 9108 9122 

49136 49150 49164 49178 49192 49206 49220 49234 49248 49262 

9276 9290 9304 9318 9332 9346 9360 9374 9388 9402 

9415 9429 9443 9457 9471 9485 9499 9513 9527 9541 

9554 9568 9582 9596 9610 9624 9638 9651 9665 9679 

9693 9707 9721 9734 9748 9762 9776 9790 9803 9817 

9831 9845 9859 9872 9886 9900 9914 9927 9941 9955 

9969 9982 9996 50010 50024 50037 50051 50065 50079 50092 

50106 50120 50133 0147 0161 0174 0188 0202 0215 0229 

0243 0256 0270 0284 0297 0311 0325 0338 0352 0365 

0379 0393 0406 0420 0433 0447 0461 0474 0488 0501 

50515 50529 50542 50556 50569 50583 50596 50610 50623 50637 

0651 0664 0678 0691 0705 0718 0732 0745 0759 0772 

0786 0799 0813 0826 0840 0853 0866 0880 0893 0907 

0920 0934 0947 0961 0974 0987 1001 1014 1028 1041 

1055 1068 1081 1095 1108 1121 1135 1148 1162 1175 

1188 1202 1215 1228 1242 1255 1268 1282 1295 1308 

1322 1335 1348 1362 1375 1388 1402 1415 1428 1441 

1455 1468 1481 1495 1508 1521 1534 1548 1561 1574 

1587 1601 1614 1627 1640 1654 1667 1680 1693 1706 

1720 1733 1746 1759 1772 1786 1799 1812 1825 1838 

51851 51865 51878 51891 51904 51917 51930 51943 51957 51970 

1983 1996 2009 2022 2035 2048 2061 2075 2088 2101 

2114 2127 2140 2153 2166 2179 2192 2205 2218 2231 

2244 2257 2270 2284 2297 2310 2323 2336 2349 2362 

2375 2388 2401 2414 2427 2440 2453 2466 2479 2492 

2504 2517 2530 2543 2556 2569 2582 2595 2608 2621 

2634 2647 2660 2673 2686 2699 2711 2724 2737 2750 

2763 2776 2789 2802 2815 2827 2840 2853 2866 2879 

2892 2905 2917 2930 2943 2956 2969 2982 2994 3007 

3020 3033 3046 3058 3071 3084 3097 3110 3122 3135 

53148 53161 53173 63186 53199 53212 53224 53237 53250 53263 

3275 3288 3301 3314 3326 3339 3352 3364 3377 3390 

3403 3415 3428 3441 3453 3466 3479 3491 3504 3517 

3529 3542 3555 3567 3580 3593 3605 3618 3631 3643 

3656 3668 3681 3694 3706 3719 3732 3744 3757 3769 

3782 3794 3807 3820 3832 3845 3857 3870 3882 3895 

3908 3920 3933 3945 3958 3970 3983 3995 4008 4020 

4033 4045 4058 4070 4083 4095 4108 4120 4133 4145 

4158 4170 4183 4195 4208 4220 4233 4245 4258 4270 

4283 4295 4307 4320 4332 4345 4357 4370 4382 4394 

54407 54419 54432 64444 64466 64469 64481 54494 54506 54518 



496 


TABLE VT.— LOGARITHMS OF NUMBERS. 


: N 


12 34 567 89 


350 


54407 54419 54432 54444 54456 54469 54481 54494 54506 54518 


1 


4531 4543 4555 4568 4580 4593 4605 4617 4630 4642 


2 


4654 4667 4679 4691 4704 4716 4728 4741 4753 4765 


3 


4777 4790 4802 4814 4827 4839 4851 4864 4876 4888 


4 


4900 4913 4925 4937 4949 4962 4974 4986 4998 5011 


6 


5023 5035 5047 5060 5072 5084 5096 5108 5121 5133 


6 


5145 5157 5169 5182 5194 5206 5218 5230 5242 5255 


7 


5267 5279 5291 5303 5315 5328 5340 5352 5364 5376 


8 


5388 5400 5413 5425 5437 5449 5461 5473 5485 5497 


9 


5509 5522 5534 5546 5558 6570 5582 5594 6606 5618 


360 


55630 55642 55654 65666 55678 55691 55703 55715 65727 56739 


1 


5751 5763 5775 5787 5799 5811 5823 5835 5847 5859 


2 


5871 5883 5895 5907 5919 5931 6943 6955 6967 5979 


3 


6991 6003 6015 6027 6038 6050 6062 6074 6086 6098 


4 


6110 6122 6134 6146 6158 6170 6182 6194 6205 6217 


5 


6229 6241 6253 6265 6277 6289 6301 6312 6324 6336 


6 


6348 6360 6372 6384 6396 6407 6419 6431 6443 6455 


7 


6467 6478 6490 6502 6514 6526 6538 6549 6561 6573 


8 


6585 6597 6608 6620 6632 6644 6656 6667 6679 6691 


9 


6703 6714 6726 6738 6750 6761 6773 6785 6797 6808 


370 


56820 56832 66844 66855 56867 56879 56891 56902 56914 56926 


1 


6937 6949 6961 6972 6984 6996 7008 7019 7031 7043 


2 


7054 7066 7078 7089 7101 7113 7124 7136 7148 7169 


3 


717i 7183 7194 7206 7217 7229 7241 7252 7264 7276 


4 


7287 7299 7310 7322 7334 7345 7357 7368 7380 7392 


5 


7403 7415 7426 7438 7449 7461 7473 7484 7496 7507 


6 


7519 7530 7542 7553 7565 7576 7588 7600 7611 7623 


7 


7634 7646 7657 7669 7680 7692 7703 7715 7726 7738 


8 


7749 7761 7772 7784 7795 7807 7818 7830 7841 7852 


9 


7864 7875 7887 7898 .7910 7921 7933 7944 7965 7967 


380 


57978 67990 68001 58013 58024 58036 68047 58058 68070 68081 


1 


8092 8104 8115 8127 8138 8149 8161 8172 8184 8195 


2 


8206- 8218 8229 8240 8252 8263 8274 8286 8297 8309 


3 


.8320 8331 8343 8354 8365 8377 8388 8399 8410 8422 


4 


8433 8444 8456 8467 8478 8490 8501 8612 8524 8535 


6 


8546 8557 8569 8580 8591 8602 8614 8625 8636 8647 


6 


8659 8670 8681 8692 8704 8715 8726 8737 8749 8760 


7 


8771 8782 8794 8805 8816 8827 8838 8850 8861 8872 


8 


8883 8894 8906 8917 8928 8939 8950 8961 8973 8984 


9 


8995 9006 9017 9028 9040 9061 9062 9073 9084 9096 


390 


59106 59118 69129 59140 69151 59162 69173 59184 59195 59207 


1 


9218 9229 9240 9251 9262 9273 9284 9295 9306 9318 


2 


9329 9340 9351 9362 «373 9384 9396 9406 9417 9428 


3 


9439 9450 9461 9472 9483 9494 9506 9517 9528 9539 


4 


9550 9561 9572 9583 9594 9605 9616 9627 9638 9649 


5 


9660 9671 9682 9693 9704 9715 9726 9737 9748 9759 


6 


9770 9780 9791 9802 9813 9824 9836 9846 9857 9868 


7 


9879 9890 9901 9912 9923 9934 9945 9956 9966 9977 


8 


9988 9999 60010 60021 60032 60043 60064 60065 60076 60086 


9 


60097 60108 0119 0130 0141 0162 0163 0173 0184 0195 
60206 60217 60228 60239 60249 60260 60271 60282 60293 60304 


400 





TABLE VI.— LOGARITHMS OF NUISIBERS, 497 


N 


0123456789 

• 


400 


60206 60217 60228 60239 60249 60200 60271 60282 60293 60304 


1 


0314 0325 0336 0347 0358 0369 0379 0390 0401 0412 


2 


0423 0433 0444 0455 0466 0477 0487 0498 0509 0520 


3 


0531 0541 0552 0563 0574 0584 0595 0606 0617 0627 


4 


0638 0649 0660 0670 0681 0692 0703 0713 0724 0735 


5 


0746 0756 0767 0778 0788 0799 0810 0821 0831 0842 


6 


0853 0863 0874 0885 0895 0906 0917 0927 0938 0949 


7 


0959 0970 0981 0991 1002 1013 1023 1034 1045 1055 


8 


1066 1077 1087 1098 1109 1119 1130 1140 1151 1162 


9 


1172 1183 1194 1204 1215 1225 1236 1247 1257 1268 


410 


61278 61289 61300 61310 61321 61331 61342 61352 61363 61374 


1 


1384 1395 1405 1416 1426 1437 1448 1458 1469 1479 


2 


1490 1500 1511 1521 1532 1542 1553 1563 1574 1584 


3 


1595 1606 1616 1627 1637 1648 1658 1669 1679 1690 


4 


1700 1711 1721 1731 1742 1752 1763 1773 1784 1794 


5 


1805 1815 1826 1836 1847 1857 1868 1878 1888 1899 


6 


1909 1920 1930 1941 1951 1962 1972 1982 1993 2003 


7 


2014 2024 2034 2045 2055 2066 2076 2086 2097 2107 


8 


2118 2128 2138 2149 2159 2170 2180 2190 2201 2211 


9 


2221 2232 2242 2252 2263 2273 2284 2294 2304 2315 


420 


62325 62335 62346 62356 62366 62377 62387 62397 62408 62418 


1 


2428 2439 2449 2459 2469 2480 2490 2500 2511 2521 


2 


2531 2542 2552 2562 2572 2583 2593 2603 2613 2624 


3 


2634 2644 2655 2665 2675 2685 2696 2706 2716 2726 


4 


2737 2747 2757 2767 2778 2788 2798 2808 2818 2829 


5 


2839 2849 2859 2870 2880 2890 2900 2910 2921 2931 


6 


2941 2951 2961 2972 2982 2992 3002 3012 3022 3033 


7 


3043 3053 3063 3073 3083 3094 3104 3114 3124 3134 


8 


3144 3155 3165 3175 3185 3195 3205 3215 3225 3236 


9 


3246 3256 3266 3276 3286 3296 3306 3317 3327 3337 


430 


63347 63357 63367 63377 63387 63397 63407 63417 63428 63438 


1 


3448 3458 3468 3478 3488 3498 3508 3518 3528 3538 


2 


3548 3558 3568 3579 3589 3599 3609 3619 3629 3639 


3 


3649 3659 3669 3679 3689 3699 3709 3719 3729 3739 


4 


3749 3759 3769 3779 3789 3799 3809 3819 3829 3839 


5 


3849 3859 3869 3879 3889 3899 3909 3919 3929 3939 


6 


3949 3959 3969 3979 3988 3998 4008 4018 4028 4038 


7 


4048 4058 4068 4078 4088 4098 4108 4118 4128 4137 


8 


4147 4157 4167 4177 4187 4197 4207 4217 4227 4237 


9. 


4246 4256 4266 4276 4286 4296 4306 4316 4326 4335 


440 


64345 64355 64365 64375 64385 64395 64404 64414 64424 64434 


1 


4444 4454 4464 4473 4483 4493 4503 4513 4523 4532 


2 


4542 4552 4562 4572 4582 4591 4601 4611 4621 4631 


3 


4640 4650 4660 4670 4680 4689 4699 4709 4719 4729 


4 


4738 4748 4758 4708 4777 4787 4797 4807 4816 4820 


5 


4836 4846 4856 4805 4875 4885 4895 4904 4914 4924 


6 


4933 4943 4953 4963 4972 4982 4992 5002 5011 5021 


7 


5031 5040 5050 5060 5070 5079 5089 5099 5108 5118 


8 


5128 5137 5147 5157 5167 5176 5186 5196 5205 5215 


9 


5225 5234 5244 5254 5263 5273 5283 5292 5302 5312 


450 


65321 65331 65341 65350 65360 65369 65379 65389 65398 65408 



498 


TABLE VI.— LOGARITHMS OF NUMBERS. 


N 


O 1 2 3 


4 5 6 7 8 9 1 

* 1 


^50 


65321 65331 65341 65350 65360 65369 65379 65389 65398 65408 


1 


5418 5427. 5437 5447 


5456 5466 6475 6485 5495 6604 


2 


5514 5523 5533 6543 


5552 6562 6671 6581 5591 5600 


3 


6610 5619 5629 5639 


5648 6658 5667 6677 6686 5696 


4 


5706 5715 5725 6734 


6744 6753 5763 5772 6782 6792 


5 


6801 5811 6820 5830 


6839 6849 6858 5868 5877 6887 


6 


5896 6906 5916 6926 


5935 5944 5954 6963 5973 5982 


7 


5992 6001 6011 6020 


6030 6039 6049 6058 6068 6077 


8 


6087 6096 6106 6115 


6124 6134 6143 6163 6162 6172 


9 


6181 6191 6200 6210 


6219 6229 6238 6247 6257 6266 


460 


66276 66285 66295 66304 66314 66323 66332 66342 66351 66361 


1 


6370 6380 6389 6398 


6408 6417 6427 6436 6445 6455 


2 


6464 6474 6483 6492 


6502 6611 6521 6530 6539 6549 


3 


6558 6567 6577 6586 


6596 6605 6614 6624 6633 6642 


4 


6652 6661 6671 6680 


6689 6699 6708 6717 6727 6736 


5 


6745 6755 6764 6773 


67B3 6792 6801 6811 6820 6829 


6 


6839 6848 6857 6867 


6876 6885 6894 6904 6913 6922 


1 


6932 6941 6950 6960 


6969 6978 6987 6997 7006- 7016 


8 


7025 7034 7043 7052 


7062 7071 7080 7089 7099 7108 


9 


7117 7127 7136 7146 


7164 7164 7173 7182 7191 7201 


470 


67210 67219 67228 67237 67247 67256 67265 67274 67284 67293 


1 


7302 7311 7321 7330 


7339 7348 7357 7367 7376 7385 


2 


7394 7403 7413 7422 


7431 7440 7449 7459 7468 7477 


3 


7486 7495 7504 7514 


7623 7632 7541 7550 7560 7569 


4 


7578 7587 7596 7605 


7614 7624 7633 7642 7651 7660 


5 


7669 7679 7688 7697 


7706 7715 7724 7733 7742 7762 


6 


7761 7770 7779 7788 


7797 7806 7816 7825 7834 7843 


7 


7852 7861 7870 7879 


7888 7897 7906 7916 7925 7934 


8 


7943 7952 7961 7970 


7979 7988 7997 8006 8016 8024 


9 


8034 8043 8052 8061 


8070 8079 8088 8097 8106 8115 


480 


68124 68133 68142 68161 


68160 68169 68178 68187 68196 68206 


1 


8215 8224 8233 8242 


8251 8260 8269 8278 8287 8296 


2 


8305 8314 8323 8332 


8341 8350 8359 8368 8377 8386 


3 


8395 8404 8413 8422 


8431 8440 8449 8458 8467 8476 


4 


8485 8494 8502 8511 


8520 8529 8538 8547 8656 8565 


5 


8574 8583 8592 8601 


8610 8619 8628 8637 8646 8655 


6 


8664 8673 8681 8690 


8699 8708 8717 8726 8735 8744 


7 


,8753 8762 8771 8780 


8789 8797 8806 8815 8824 8833 


8 


8842 8851 8860 8869 


8878 8886 8895 8904 8913 8922 


9 


8931 8940 8949 8958 


8966 8976 8984 . 8993 9002 9011 


490 


69020 69028 69037 69046 69055 69064 69073 69082 69090 69099 


1 


9108 9117 9126 9135 


9144 9162 9161 9170 9179 9188 


2 


9197 9205 9214 9223 


9232 9241 9249 9268 9267 9276 


3 


9285 9294 9302 9311 


9320 9329 9338 9346 9356 9364' 


4 


9373 9381 9390 9399 


9408 9417 9425 9434 9443 9452 


5 


9461 9469 9478 9487 


9496 9504 9613 9622 9531 9539 


6 


9548 9557 9566 9574 


9583 9592 9601 9609 9618 9627 


7 


9636 9644 9653 9662 


9671 9679 9688 9697 9705 9714 


8 


9723 9732 9740 9749 


9758 9767 9775 9784 9793 9801 


9 


9810 9819 9827 9836 


9845 9854 9862 9871 9880 9888 


500 


69897 69906 69914 69923 69932 69940 69949 69958 09966 69975 



TABLE VI.— LOGARITHMS OF NUMBERS. 499 



N 


012 3 456789 


500 


69897 69906. 69914 69923 69932 69940 69949 69958 69966 69975 


1 


9984 9992 70001 70010 70018 70027 70036 70044 70053 70062 


2 


70070 70079 0088 0096 0105 0114 0122 0131 0140 0148 


3 


0157 0165 0174 0183 0191 0200 0209 0217 0226 0234 


4 


0243 0252 0260 0269 0278 0286 0295 0303 0312 0321 


5 


0329 0338 0346 0355 0364 0372 0381 0389 0398 0406 


6 


0415 0424 0432 0441 0449 0458 0467 0475 0484 0492 


7 


0501 0509 0518 0526 0535 0544 0552 0561 0569 0578 


8 


0586 0595 0603 0612 0621 0629 0638 0646 0655 0663 


9 


0672 0680 0689 0697 0706 0714 0723 0731 0740 0749 


510 


70757 70766 70774 70783 70791 70800 70808 70817 70825 70834 


1 


0842 0851 0859 0868 0876 0885 0893 0902 0910 0919 


2 


0927 0935 0944 0952 0961 0969 0978 0986 0995 1003 


3 


1012 1020 1029 1037 1046 1054 1063 1071 1079 1088 


4 


1096 1105 1113 1122 1130 1139 1147 1155 1164 1172 


5 


1181 1189 1198 1206 1214 1223 1231 1240 1248 1257 


6 


1265 1273 1282 1290 1299 1307 1315 1324 1332 1341 


7 


1349 1357 1366 1374 1383 1391 1399 1408 1416 1425 


8 


1433 1441 1450 1458 1466 1475 1483 1492 1500 1508 


9 


1517 1525 1533 1542 1550 1559 1567 1575 1584 1592 


620 


71600 71609 71617 71625 71634 71642 71650 71659 71667 71675 


1 


1084 1692 1700 1709 1717 1725 1734 1742 1750 1759 


2 


1767 1775 1784 1792 1800 1809 1817 1825 1834 1842 


3 


1850 1858 1867 1875 1883 1892 1900 1908 1917 1925 


4 


1933 1941 1950 1958 1966 1975 1983 1991 1999 2008 


5 


2016 2024 2032 2041 2049 2057 2066 2074 2082 2090 


6 


2099 2107 2115 2123 2132 2140 2148 2156 2165 2173 


7 


2181 2189 2198 2206 2214 2222 2230 2239 2247 2255 


8 


2263 2272 2280 2288 2296 2304 2313 2321 2329 2337 


9 


2346 2354 2362 2370 2378 2387 2395 2403 2411 2419 


530 


72428 72436 72444 72452 72460 72469 72477 72485 72493 72501 


1 


2509 2518 2526 2534 2542 2550 2558 2567 2575 2583 


2 


2591 2599 2607 2616 2624 2632 2640 2648 2656 2665 


3 


2673 2681 2689 2697 2705 2713 2722 2730 2738 2746 


4 


2754 2762 2770 2779 2787 2795 2803 2811 2819 2827 


5 


2835 2843 2852 2860 2868 2876 2884 2892 2900 2908 


6 


2916 2925 2933 2941 2949 2957 2965 2973 2981 2989 


7 


2997 3006 3014 3022 3030 3038 3046 3054 3062 3070 


8 


3078 3086 3094 3102 3111 3119 3127 3135 3143 3151 


9 


3159 3167 3175 3183 3191 3199 3207 3215 3223 3231 


540 


73239 73247 73255 73263 73272 73280 73288 73296 73304 73312 


1 


3320 3328 3336 3344 3352 3360 3308 3376 3384 3392 


2 


3400 3408 3416 3424 3432 3440 3448 3456 3464 3472 


3 


3480 3488 3496 3504 3512 3520 3528 3536 3544 3552 


4 


3560 3568 3576 3584 3592 3600 3608 3616 3624 3632 


5 


3640 3648 3656 3664 3672 3679 3687 3095 3703 3711 


6 


3719 3727 3735 3743 3751 3759 3767 3775 3783 3791 


7 


3799 3807 3815 3823 3830 3838 3846 3854 3862 3870 


8 


3878 3886 3894 3902 3910 3918 3926 3933 3941 3949 


9 


3957 3965 3973 3981 3989 3997 4005 4013 4020 4028 


550 


74036 74044 74052 74060 74068 74076 74084 74092 74099 74107 



500 


TABLE VL— LOGARITHMS OF NUMBERS. 


N 


0123456789 


650 


74036 74044 74052 74060 74068 74076 74084 74092 74099 74107 


1 


4115 4123 4131 4139 4147 4155 4162 4170 4178 4186 


2 


4194 4202 4210 4218 4225 4233 4241 4249 4257 4265 


3 


4273 4280 4288 4296 4304 4312 4320 4327 4335 4343 


4 


4351 4359 4367 4374 4382 4390 4398 4406 4414 4421 


5 


4429 4437 4445 4453 4461 4468 4476 4484 4492 4500 


6 


4507 4515 4523 4531 4539 4547 4554 4562 4570 4578 


7 


4586 4593 4601 4609 4617 4624 4632 4640 4648 4656 


8 


4663 4671 4679 4687 4695 4702 4710 4718 4726 4733 


9 


4741 4749 4757 4764 4772 4780 4788 4796 4803 4811 


560 


74819 74827 74834 74842 74850 74858 74865 74873 74881 74889 


1 


4896 4904 4912 4920 4927 4935 4943 4950 4958 4966 


2 


4974 4981 4989 4997 5005 5012 5020 5028 5035 5043 


3 


5051 5059 5066 5074 5082 5089 5097 5105 5113 5120 


4 


5128 5136 5143 5151 5159 5166 5174 5182 5189 5197 


5 


5205 5213 5220 5228 5236 5243 5251 5259 6266 5274 


6 


5282 5289 5297 5305 5312 5320 5328 5335 5343 5351 


7 


5358 5366 5374 5381 5389 5397 5404 5412 5420 5427 


8 


5435 5442 5450 5458 5465 6473 6481 5488 6496 5604 


9 


6511 5619 5626 6534 6542 6549 5557 5565 5672 6680 


570 


75587 75595 76603 75610 75618 76626 76633 76641 75648 75666 


1 


5664 5671 5679 5686 6694 5702 6709 6717 6724 5732 


2 


5740 5747 5755 5762 5770 5778 5785 5793 6800 6808 


3 


5815 5823 5831 5838 5846 6853 6861 5868 5876 5884 


4 


5891 5899 5906 5914 6921 5929 5937 5944 6952 5969 


5 


6967 5974 5982 6989 6997 6005 6012 6020 6027 603i 


6 


6042 6050 6067 6065 6072 6080 6087 6095 6103 6110 


7 


6118 6125 6133 6140 6148 6155 6163 6170 6178 6185 


8 


6193 6200 6208 6215 6223 6230 6238 6245 6253 6260 


9 


6268 6276 6283 6290 6298 6306 6313 6320 6328 6336 


580 


76343 76350 76358 76366 76373 76380 76388 76395 76403 76410 


1 


6418 6425 6433 6440 6448 6455 6462 6470 6477 6485 


2 


6492 6500 6507 6515 6522 6530 6537 6545 6552 6559 


3 


6567 6574 6582 6589 6597 6604 6612 6619 6626 6634 


4 


6641 6649 6656 6664 6671 6678 6686 6693 6701 6708 


5 


6716 6723 6730 6738 6745 6753 6760 6768 6775 6782 


6 


6790 6797 6805 6812 6819 6827 6834 6842 6849 6866 


7 


6864 6871 6879 6886 6893 6901 6908 6916 6923 6930 


8 


6938 6946 6953 6960 6967 6975 6982 6989 6997 7004 


9 


7012 7019 7026 7034 7041 7048 7056 7063 7070 7078 


590 


77085 77093 77100 77107 77115 77122 77129 77137 77144 77151 


1 


7159 7166 7173 7181 7188 7195 7203 7210 7217 7225 


2 


7232 7240 7247 7254 7262 7269 7276 7283 7291 7298 


3 


7306 7313 7320 7327 7335 7342 7349 7357 7364 7371 


4 


7379 7386 7393 7401 7408 7415 7422 7430 7437 7444 


5 


7452 7459 7466 7474 7481 7488 7495 7503 7510 7517 


6 


7525 7532 7539 7546 7554 7561 7568 7576 7583 7690 


7 


7597 7605 7612 7619 7627 7634 7641 7648 7656 7663 


8 


7670 7677 7685 7692 7699 7706 7714 7721 7728 7735 


9 


7743 7750 7757 7764 7772 7779 7786 7793 7801 7808 


600 


77816 77822 77830 77837 77844 77851 77869 77866 77873 77880 





TABLE VI,— LOGARITHMS OF NUMBER? 


). 


501 


N 


O 1 2 3 4 5 6 


7 


8 


9 


600 


77815 77822 77830 77837 77844 77851 77859 77866 77873 77880 


1 


7887 7895 7902 7909 7916 7924 7931 


7938 


7945 


7952 


2 


7960 7967 7974 7981 7988 7996 8003 


8010 


8017 


8025 


3 


8032 8039 8046 8053 8061 8068 8075 


8082 


8089 


8097 


4 


8104 8111 8118 8125 8132 8140 8147 


8154 


8161 


8168 


5 


8176 8183 8190 8197 8204 8211 8219 


8226 


8233 


8240 


6 


8247 8254 8262 8269 8276 8283 8290 


8297 


8305 


8312 


7 


8319 8326 8333 8340 8347 8355 8362 


8369 


8376 


8383 


8 


8390 8398 8405 8412 8419 8426 8433 


8440 


8447 


8455 


9 


8462 8469 8476 8483 8490 8497 8504 


8512 


8519 


8526 


610 


78533 78540 78547 78554 78561 78569 78576 78583 78590 


78597 


1 


8604 8611 8618 8625 8633 8640 8647 


8654 


8661 


8668 


2 


8675 8682 8689 8696 8704 8711 8718 


8725 


8732 


8739 


3 


8746 8753 8760 8767 8774 8781 8789 


8796 


8803 


8810 


4 


8817 8824 8831 8838 8845 8852 8859 


8866 


8873 


8880 


5 


8888 8895 8902 8909 8916 8923 8930 


8937 


8944 


8951 


6 


8958 8965 8972 8979 8986 8993 9000 


9007 


9014 


9021 


7 


9029 9036 9043 9050 9057 9064 9071 


9078 


9085 


9092 


8 


9099 9106 9113 9120 9127 9134 9141 


9148 


9155 


9162 


9 


9169 9176 9183 9190 9197 9204 9211 


9218 


9225 


9232 


620 


79239 79246 79253 79260 79267 79274 79281 


79288 


79295 79302 


1 


9309 9316 9323 9330 9337 9344 9351 


9358 


9365 


9372 


2 


9379 9386 9393 9400 9407 9414 9421 


9428 


9435 


9442 


3 


9449 9456 9463 9470 9477 9484 9491 


9498 


9505 


9511 


4 


9518 9525 9532 9539 9546 9553 9560 


9567 


9574 


9581 


5 


9588 9595 9602 9609 9616 9623 9630 


9637 


9644 


9650 


6 


9657 9664 9671 9678 9685 9692 9699 


9706 


9713 


9720 


7 


9727 9734 9741 9748 9754 9761 9768 


9775 


9782 


9789 


8 


9796 9803 9810 9817 9824 9831 9837 


9844 


9851 


9858 


9 


9865 9872 9879 9886 9893 9900 9906 


9913 


9920 


9927 


630 


79934 79941 79948 79955 79962 79969 79975 79982 


79989 79996 


1 


80003 80010 80017 80024 80030 80037 80044 80051 80058 80065 | 


2 


0072 0079 0085 0092 0099 0106 0113 


0120 


0127 


0134 


3 


0140 0147 0154 0161 0168 0175 0182 


0188 


0195 


0202 


4 


0209 0216 0223 0229 0236 0243 0250 


0257 


0264 


0271 


5 


0277 0284 0291 0298 0305 0312 0318 


0325 


0332 


0339 


6 


0346 0353 0359 0366 0373 0380 0387 


0393 


0400 


0407 


7 


0414 0421 0428 0434 0441 0448 0455 


0462 


0468 


0475 


8 


0482 0489 0496 0502 0509 0516 0523 


0530 


0536 


0543 


9 


0550 0557 0564 0570 0577 0584 0591 


0598 


0604 


0611 


640 


80618 80625 80632 80638 80645 80652 80659 80665 80672 80679 


1 


0686 0693 0699 0706 0713 0720 0726 


0733 


0740 


0747 


2 


0754 0760 0767 0774 0781 0787 0794 


0801 


0808 


0814 


3 


0821 0828 0835 0841 0848 0855 0862 


0868 


0875 


0882 


4 


0889 0895 0902 0909 0916 0922 0929 


0936 


0943 


0949 


5 


0956 0963 0969 0976 0983 0990 0996 


1003 


1010 


1017 


8 


1023 1030 1037 1043 1050 1057 1064 


1070 


1077 


1084 


7 


1090 1097 1104 1111 1117 1124 1131 


1137 


1144 


1151 


8 


1158 1164 1171 1178 1184 1191 1198 


1204 


1211 


1218 


9 


1224 1231 1238 1245 1251 1258 1265 


1271 


1278 


1285 


650 


81291 81298 8130i 81311 81318 81325 81331 81338 81345 81351 



502 TABLE VI.— LOGARITHMS OF NUMBEK8. 



N 


012 34 567 8 9 


650 


81291 81298 81305 81311 81318 81325 81331 81338 81345 81351 


1 


1358 1365 1371 1378 1385 1391 1398 1405 1411 1418 


2 


1425 1431 1438 1445 1451 1458 1465 1471 1478 1485 


3 


1491 1498 1505 1511 1518 1525 1531 1538 1544 1551 


4 


1558 1564 1571 1578 1584 1591 1598 1604 1611 1617 


5 


1624 1631 1637 1644 1651 1657 1664 1671 1677 1684 


6 


1690 1697 1704 1710 1717 1723 1730 1737 1743 1750 


7 


1757 1763 1770 1776 1783 1790 1796 1803 1809 1816 


8 


1823 1829 1836 1842 1849 1856 1862 1869 1875 1882 


9 


1889 1895 1902 1908 1915 1921 1928 1935 1941 1948 


660 


81954 81961 81968 81974 81981 81987 81994 82000 82007 82014 


1 


2020 2027 2033 2040 2046 2053 2060 2066 2073 2079 


2 


2086 2092 2099 2105 2112 2119 2125 2132 2138 2145 


3 


2151 2158 2164 2171 2178 2184 2191 2197 2204 2210 


4 


2217 2223 2230 2236 2243 2249 2256 2263 2269 2276 


5 


2282 2289 2295 2302 2308 2315 2321 2328 2334 2341 


6 


2347 2354 2360 2367 2373 2380 2387 2393 2400 2406 


7 


2413 2419 2426 2432 2439 2445 2452 2458 2465 2471 


8 


2478 2484 2491 2497 2504 2510 2517 2523 2530 2536 


9 


2543 2549 2556 2562 2569 2575 2582 2588 2595 2601 


670 


82607 82614 82620 82627 82633 82640 82646 82653 82659 82666 


1 


2672 2679 2685 2692 2698 2705 2711 2718 2724 2730 


2 


2737 2743 2750 2756 2763 2769 2776 2782 2789 2795 


3 


2802 2808 2814 2821 2827 2834 2840 2847 2853 2860 


4 


2866 2872 2879 2885 2892 2898 2905 2911 2918 2924 


5 


2930 2937 2943 2950 2956 2963 2969 2975 2982 2988 


6 


2995 3001 3008 3014 3020 3027 3033 3040 3046 3052 


7 


3059 3065 3072 3078 3085 3091 3097 3104 3110 3117 


8 


3123 3129 3136 3142 3149 3155 3161 3168 3174 3181 


9 


3187 3193 3200 3206 3213 3219 3225 3232 3238 3245 


680 


83251 83257 83264 83270 83276 83283 83289 83296 83302 83308 


1 


3315 3321 3327 3334 3340 3347 3353 3359 3366 3372 


2 


3378 3385 3391 3398 3404 3410 3417 3423 3429 3436 


3 


3442 3448 3455 3461 3467 3474 3480 3487 3493 3499 


4 


3506 3512 3518 3525 3531 3537 3544 3550 3556 3563 


5 


3569 3575 3582 3588 3594 3601 3607 3613 3620 3626 


6 


3632 3639 3645 3651 3658 3664 3670 3677 3683 3689 


7 


3696 3702 3708 3715 3721 3727 3734 3740 3746 3753 


8 


3759 3765 3771 3778 3784 3790 3797 3803 3809 3816 


9 


3822 3828 3835 3841 3847 3853 3860 3866 3872 3879 


690 


83885 83891 83897 83904 83910 83916 83923 83929 83935 83942 


1 


3948 3954 3960 3967 3973 3979 3985 3992 3998 4004 


2 


4011 4017 4023 4029 4036 4042 4048 4055 4061 4067 


3 


4073 4080 4086 4092 4098 4105 4111 4117 4123 4130 


4 


4136 4142 4148 4155 4161 4167 4173 4180 4186 4192 


5 


4198 4205 4211 4217 4223 4230 4236 4242 4248 4255 


6 


4261 4267 4273 4280 4286 4292 4298 4305 4311 4317 


7 


4323 4330 4336 4342 4348 4354 4361 4367 4373 4379 


8 


4386 4392 4398 4404 4410 4417 4423 4429 4435 4442 


9 


4448 4454 4460 4466 4473 4479 4485 4491 4497 4504 


700 


84510 84516 84522 84528 84535 84541 84547 84553 84559 84566 



TABLE VI.— LOGARITHMS OF NUMBERS. 



503 



N 
700 


0123456789 


84510 84516 84522 84528 84535 84541 84547 84553 84559 84566 


1 


4572 4578 4584 4590 4597 4603 4609 4615 4621 4628 


2 


4634 4640 4646 4652 4658 4665 4671 4677 4683 4689 


3 


4696 4702 4708 4714 4720 4726 4733 4739 4745 4751 


4 


4757 4763 4770 4776 4782 4788 4794 4800 4807 4813 


5 


4819 4825 4831 4837 4844 4850 4856 4862 4868 4874 


6 


4880 4887 4893 4899 4905 4911 4917 4924 4930 4936 


7 


4942 4948 4954 4960 4967 4973 4979 4985 4991 4997 


8 


5003 5009 5016 5022 5028 5034 5040 5046 5052 5058 


9 


6065 5071 5077 5083 6089 6095 6101 5107 5114 6120 


710 


85126 85132 85138 85144 85150 85156 85163 85169 85175 85181 


1 


5187 5193 5199 5205 5211 5217 5224 5230 5236 5242 


2 


5248 5254 5260 5266 5272 5278 5285 5291 5297 ' 5303 


3 


5309 5315 5321 5327 5333 5339 5345 5352 5358 5364 


4 


6370 5376 5382 5388 5394 5400 5406 6412 5418 5425 


5 


5431 5437 5443 5449 5455 5461 5467 5473 5479 6485 


6 


5491 5497 5503 5509 5516 5522 5528 5534 5540 5546 


7 


6552 5558 6564 5570 6576 6582 5588 5594 5600 5606 


8 


5612 6618 6625 5631 5637 6643 6649 5655 5661 5667 


9 


5673 5679 6685 6691 5697 6703 6709 6715 5721 5727 


720 


85733 85739 85745 85751 85757 85763 85769 85775 85781 85788 


1 


5794 6800 5806 5812 5818 6824 6830 5836 5842 5848 


2 


5854 6860 5866 5872 5878 6884 5890 5896 6902 5908 


3 


5914 6920 5926 6932 5938 6944 6950 6956 5962 5968 


4 


5974 6980 6986 5992 5998 6004 6010 6016 6022 6028 


5 


6034 6040 6046 6052 6058 6064 6070 6076 6082 6088 


6 


6094 6100 6106 6112 6118 6124 6130 6136 6141 6147 


7 


6163 6159 6165 6171 6177 6183 6189 6195 6201 6207 


8 


6213 6219 6225 6231 6237 6243 6249 6255 6261 6267 


9 


6273 6279 6285 6291 6297 6303 6308 6314 6320 6326 


730 


86332 86338 86344 86350 86356 86362 86368 86374 86380 86386 


1 


6392 6398 6404 6410 6415 6421 6427 6433 6439 6445 


2 


6451 6457 6463 6469 6475 6481 6487 6493 6499 6504 


3 


6510 6516 6522 6528 6534 6540 6546 6552 6558 6564 


4 


6570 6576 6581 6587 6593 6599 6605 6611 6617 6623 


5 


6629 6635 6641 6646 6652 6658 6664 6670 6676 6682 


6 


6688 6694 6700 6705 6711 6717 6723 6729 6735 6741 


7 


6747 6753 6759 6764 6770 6776 6782 6788 6794 6800 


8 


6806 6812 6817 6823 6829 6835 6841 6847 6853 6859 


9 


6864 6870 6876 6882 6888 6894 6900 6906 6911 6917 


740 


86923 86929 86935 86941 86947 86953 86958 86964 86970 86976 


1 


6982 6988 6994 6999 7005 7011 7017 7023 7029 7035 


2 


7040 7046 7052 7058 7064 7070 t075 7081 7087 7093 


3 


7099 7105 7111 7116 7122 7128 7134 7140 7146 7151 


4 


7157 7163 7169 7175 7181 7186 7192 7198 7204 7210 


5 


7216 7221 7227 7233 7239 7245 7251 7256 7262 7268 


6 


7274 7280 7286 7291 7297 7303 7309 7315 7320 7326 


7 


7332 7388 7344 7349 7355 7361 7367 7373 7379 7384 


8 


7390 7396 7402 7408 7413 7419 7425 7431 7437 7442 


9 


7448 7454 7460 7466 7471 7477 7483 7489 7495 7600 


750 


87506 87512 87518 87523 87529 87535 87641 87547 87552 87558 



504 TABLE VI.— LOGARITHMS OF NUMBERS. 



750 


123456789 


87506 87512 87518 87523 87529 87535 87541 87547 87552 87558 


1 


7564 7570 7576 7581 7587 7593 7599 7604 7610 7616 


2 


7622 7628 7633 7639 7645 7651 7656 7662 7668 7674 


3 


7679 7685 7691 7697 7703 7708 7714 7720 7726 7731 


4 


7737 7743 7749 7754 7760 7766 7772 7777 7783 7789 


5 


7795 7800 7806 7812 7818 7823 7829 7835 7841 7846 


6 


7852 7858 7864 7869 7875 7881 7887 7892 7898 7904 


7 


7910 7915 7921 7927 7933 7938 7944 7950 7955 7961 


8 


7967 7973 7978 7984 7990 7996 8001 8007 8013 8018 


9 


8024 8030 8036 8041 8047 8053 8058 8064 8070 8076 


760 


88081 88087 88093 88098 88104 88110 88116 88121 88127 88133 


1 


8138 8144 8150 8156 8161 8167 8173 8178 8184 8190 


2 


• 8195 8201 8207 8213 8218 8224 8230 8235 8241 8247 


3 


8252 8258 8264 8270 8275 8281 8287 8292 8298 8304 


4 


8309 8315 8321 8326 8332 8338 8343 8349 8355 8360 


5 


8366 8372 8377 8383 8389 8395 8400 8406 8412 8417 


6 


8423 8429 8434 8440 8446 8451 8457 8463 8468 8474 


7 


8480 8485 8491 8497 8502 8508 8513 8519 8525 8530 


8 


8536 8542 8547 8553 8559 8564 8570 8576 8581 8587 


9 


8593 8598 8604 8610 8615 8621 8627 8632 8638 8643 


770 


88649 88655 88660 88666 88672 88677 88683 88689 88694 88700 


1 


8705 8711 8717 8722 8728 8734 8739 8745 8750 8756 


2 


8762 8767 8773 8779 8784 8790 8795 8801 8807 8812 


3 


8818 8824 8829 8835 8840 8846 8852 8857 8863 8868 


4 


8874 8880 8885 8891 8897 8902 8908 8913 8919 8925 


5 


8930 8936 8941 8947 8953 8958 8964 8969 8975 8981 


6 


8986 8992 8997 9003 9009 9014 9020 9025 9031 9037 


7 


9042 9048 9053 9059 9064 9070 9076 9081 9087 9092 


8 


9098 9104 9109 9115 9120 9126 9131 9137 9143 9148 


9 


9154 9159 9165 9170 9176 9182 9187 9193 9198 9204 


780 


89209 89215 89221 89226 89232 89237 89243 89248 89254 89260 


1 


9265 9271 9276 9282 9287 9293 9298 9304 9310 9315 


2 


9321 9326 9332 9337 9343 9348 9354 9360 9365 9371 


3 


9376 9382 9387 9393 9398 9404 9409 9415 9421 9426 


4 


9432 9437 9443 9448 9454 9459 9465 9470 9476 9481 


5 


9487 9492 9498 9504 9509 9515 9520 9526 9531 9537 


6 


9542 9548 9553 9559 9564 9570 9575 9581 9586 9592 


7 


9597 9603 9609 9614 9620 9625 9631 9636 9642 9647 


8 


9653 9658 9664 9669 9675 9680 9686 9691 9697 9702 


9 


9708 9713 9719 9724 9730 9735 9741 9746 9752 9757 


790 


89763 89768 89774 89779 89785 89790 89796 89801 89807 89812 


1 


9818 9823 9829 9834 9840 9845 9851 9856 9862 9867 


2 


9873 9878 9883 9889 9894 9900 9905 9911 9916 9922 


3 


9927 9933 9938 9944 9949 9955 9960 9966 9971 9977 


4 


9982 9988 9993 9998 90004 90009 90015 90020 90026 90031 


5 


90037 90042 90048 90053 0059 0064 0069 0075 0080 0086 


6 


0091 0097 0102 0108 0113 0119 0124 0129 0135 0140 


7 


0146 0151 0157 0162 0168 0173 0179 0184 0189 0195 


8 


0200 0206 0211 0217 0222 0227 0233 0238 0244 024P 


9 


0255 0260 0266 0271 0276 0282 0287 0293 0298 0304 


800 


90309 90314 90320 90325 90331 90336 90342 90347 90352 90358 





TABLE VI.— LOGARITHMS OF NUMBERS. 505 


N 


0123456789 


800 


90309 90314 90320 90325 90331 90336 90342 90347 90352 90358 


1 


0363 0369 0374 0380 0385 0390 0396 0401 0407 0412 


2 


0417 0423 0428 0434 0439 0445 0450 0455 0461 0466 


3 


0472 0477 0482 0488 0493 0499 0504 0509 0515 0520 


4 


0526 0531 0536 0542 0547 0553 0558 0563 0569 0574 


5 


0580 0585 0590 0596 0601 0607 0612 0617 0623 0628 


6 


0634 0639 0644 0650 0655 0660 0666 0671 0677 0682 


7 


0687 0693 0698 0703 0709 0714 0720 0725 0730 0736 


8 


0741 0747 0752 0757 0763 0768 0773 0779 0784 0789 


9 


0795 0800 0806 0811 0816 0822 0827 0832 0838 0843 


810 


90849 90854 90859 90865 90870 90875 90881 90886 90891 90897 


1 


0902 0907 0913 0918 0924 0929 0934 0940 0945 0950 


2 


0956 0961 0966 0972 0977 0982 0988 0993 0998 1004 


3 


1009 1014 1020 1025 1030 1036 1041 1046 1052 1057 


4 


1062 1068 1073 1078 1084 1089 1094 1100 1105 1110 


5 


1116 1121 1126 1132 1137 1142 1148 1153 1158 1164 


6 


1169 1174 1180 1185 1190 1196 1201 1206 1212 1217 


7 


1222 1228 1233 1238 1243 1249 1254 1259 1265 1270 


8 


1275 1281 1286 1291 1297 1302 1307 1312 1318 1323 


9 


1328 1334 1339 1344 1350 1355 1360 1365 1371 1376 


820 


91381 91387 91392 91397 91403 91408 91413 91418 91424 91429 


1 


1434 1440 1445 1450 1455 1461 1466 1471 1477 1482 


2 


1487 1492 1498 1503 1508 1514 1519 1524 1529 1535 


3 


1540 1545 1551 1556 1561 1566 1572 1577 1582 1587 


4 


1593 1598 1603 1609 1614 1619 1624 1630 1635 1640 


5 


1645 1651 1656 1661 1666 1672 1677 1682 1687 1693 


6 


1698 1703 1709 1714 1719 1724 1730 1735 1740 1745 


7 


1751 1756 1761 1766 1772 1777 1782 1787 1793 1798 


8 


1803 1808 1814 1819 1824 1829 1834 1840 1845 1850 


9 


1855 1861 1866 1871 1876 1882 1887 1892 1897 1903 


830 


91908 91913 91918 91924 91929 91934 91939 91944 91950 91955 


1 


1960 1965 1971 1976 1981 1986 1991 1997 2002 2007 


2 


2012 2018 2023 2028 2033 2038 2044 2049 2054 2059 


3 


2065 2070 2075 2080 2085 2091 2096 2101 2106 2111 


4 


2117 2122 2127 2132 2137 2143 2148 2153 2158 2163 


5 


2169 2174 2179 2184 2189 2195 2200 2205 2210 2215 


6 


2221 2226 2231 2236 2241 2247 2252 2257 2262 2267 


7 


2273 2278 2283 2288 2293 2298 2304 2309 2314 2319 


8 


2324 2330 2335 2340 2345 2350 2355 2361 2366 2371 


9 


2376 2381 2387 2392 2397 2402 2407 2412 2418 2423 


840 


92428 92433 92438 92443 92449 92454 92459 92464 92469 92474 


1 


2480 2485 2490 2495 2500 2505 2511 2516 2521 2526 


2 


2531 2536 2542 2547 2552 2557 2562 2567 2572 2578 


3 


2583 2588 2593 2598 2603 2609 2614 2619 2624 2629 


4 


2634 2639 2645 2650 -2655 2660 2665 2670 2675 2681 


5 


2686 2691 2696 2701 2706 2711 2716 2722 2727 2732 


6 


2737 2742 2747 2752 2758 2763 2768 2773 2778 2783 


7 


2788 2793 2799 2804 2809 2814 2819 2824 2829 2834 


8 


2840 2845 2850 2855 2860 2865 2870 2875 2881 2886 


9 


2891 2896 2901 2906 2911 2916 2921 2927 2932 2937 


850 


92942 92947 92952 92957 92962 92967 92973 92978 92983 92988 



506 


TABLE VI.— LOGARITHMS OF NUMBERS. 


850 


012 3 456789 


92942 92947 92952 92957 92962 92967 92973 92978 92983 92988 


1 


2993 2998 3003 3008 3013 3018 3024 3029 3034 3039 


2 


3044 3049 3054 3059 3064 3069 3075 3080 3085 3090 


3 


3095 3100 3105 3110 3115 3120 3125 3131 3136 3141 


4 


3146 3151 3156 3161 3166 3171 3176 3181 3186 3192 


5 


3197 3202 3207 3212 3217 3222 3227 3232 3237 3242 


6 


3247 3252 3258 3263 3268 3273 3278 3283 3288 3293 


7 


3298 3303 3308 3313 3318 3323 3328 3334 3339 3344 


8 


3349 3354 3359 3364 3369 3374 3379 3384 3389 3394 


9 


3399 3404 3409 3414 3420 3425 3430 3435 3440 3445 


860 


93450 93455 93460 93465 93470 93475 93480 93485 93490 93495 


1 


3500 3505 3510 3515 3520 3526 3531 3536 3541 3546 


2 


3551 3556 3561 3566 3571 3576 3581 3586 3591 3596 


3 


3601 3606 3611 3616 3621 3626 3631 3636 3641 3646 


4 


3651 3656 3661 3666 3671 3676 3682 3687 3692 3697 


5 


3702 3707 3712 3717 3722 3727 3732 3737 3742 3747 


8 


3752 3757 3762 3767 3772 3777 3782 3787 3792 3797 


7 


3802 3807 3812 3817 3822 3827 8832 3837 3842 3847 


8 


3852 3857 3862 3867 3872 3877 3882 3887 3892 3897 


9 


3902 39e7 3912 3917 3922 3927 3932 3937 8942 3947 


870 


93952 93957 93962 93967 93972 93977 93982 93987 93992 93997 


1 


4002 4007 4012 4017 4022 4027 4032 4037 4042 4047 


2 


4052 4057 4062 4067 4072 4077 4082 4086 4091 4096 


3 


4101 4106 4111 4116 4121 4126 4131 4136 4141 4146 


4 


4151 4156 4161 4166 4171 4176 4181 4186 4191 4196 


5 


4201 4206 4211 4216 4221 4226 4231 4236 4240 4245 


6 


4250 4255 4260 4265 4270 4275 4280 4285 4290 4295 


7 


4300 4305 4310 4315 4320 4325 4330 4335 4340 4345 


8 


4349 4354 4359 4364 4369 4374 .4379 4384 4389 4394 


9 


4399 4404 4409 4414 4419 4424 4429 4433 4438 4443 


880 


94448 94453 94458 94463 94468 94473 94478 94483 94488 94493 


1 


4498 4503 4507 4512 4517 4522 4527 4532 4537 4542 


2 


4547 4552 4557 4562 4567 4571 4576 4581 4586 4591 


3 


4596 4601 4606 4611 4616 4621 4626 4630 4635 4640 


4 


4645 4650 4655 4660 4665 4670 4675 4680 4685 4689 


5 


4694 4699 4704 4709 4714 4719 4724 4729 4734 4738 


6 


4743 4748 4753 4758 4763 4768 4773 4778 4783 4787 


7 


4792 4797 4802 4807 4812 4817 4822 4827 4882 4836 


8 


4841 4846 4851 4856 4861 4866 4871 4876 4880 4885 


9 


4890 4895 4900 4905 4910 4915 4919 4924 4929 4934 


890 


94939 94944 94949 94954 94959 94963 94968 94973 94978 94983 


1 


4988 4993 4998 5002 5007 5012 5017 5022 5027 5032 


2 


5086 5041 5046 5051 5056 5061 5066 5071 6075 5080 


3 


5085 5090 5095 5100 5105 5109 5114 5119 5124 5129 


4 


5134 5189 5148 5148 515.3 5158 6163 5168 5173 5177 


5 


6182 5187 5192 5197 5202 5207 5211 5216 6221 5226 


6 


6231 6236 6240 6246 '5250 5255 5260 5265 6270 6274 


7 


5279 5284 5289 5294 5299 5303 6308 6813 5318 5823 


8 


5328 5332 5337 6342 6347 5352 5367 5861 5866 5871 


9 


5876 5381 6386 6390 5395 6400 5405 5410 5415 5419 


900 


96424 95429 95434 95439 95444 96448 95453 96468 95463 95468 





TABLE VI.— LOGARITHMS OF NUMBERS. 50? 


N 


0123456789 


900 


95424 95429 95434 95439 95444 95448 95453 95458 95463 95468 


1 


5472 5477 5482 5487 5492 6497 5501 5506 6511 6516 


2 


5521 6525 5530 6535 6640 5545 6550 6554 6559 5564 


3 


6669 6574 6578 6683 5688 5593 6698 5602 5607 5612 


4 


6617 6622 5626 5631 6636 5641 664{) 6650 6665 6660 


5 


6665 5670 6674 5679 5684 5689 5694 6698 ' 5703 5708 


6 


5713 5718 5722 6727 6732 6737 6742 6746 5751 5766 


7 


5761 6766 5770 6776 6780 6785 6789 5794 6799 5804 


8 


5809 6813 5818 5823 5828 5832 5837 6842 6847 6862 


9 


6866 5861 6866 6871 5875 5880 6885 6890 5895 5899 


910 


95904 95909 95914 95918 96923 96928 95933 96938 96942 95947 


1 


6952 6967 6961 5966 5971 5976 5980 6985 6990 6995 


2 


5999 6004 6009 6014 6019 6023 6028 6033 6038 6042 


3 


6047 6052 6057 6061 6066 6071 6076 6080 6085 6090 


4 


6095 6099 6104 6109 6114 6118 6123 6128 6133 6137 


6 


6142 6147 6152 6156 6161 6166 6171 6175 6180 6185 


6 


6190 6194 6199 6204 6209 6213 6218 6223 6227 6232 


7 


6237 6242 6246 6251 6256 6261 6265 6270 6275 6280 


8 


6284 6289 6294 6298 6303 6308 6313 6317 6322 6327 


9 


6332 6336 6341 6346 6350 6355 6360 6365 6369 6374 


920 


96379 96384 96388 96393 96398 96402 96407 96412 96417 96421 


1 


6426 6431 6435 6440 6445 6450 6454 6459 6464 6468 


2 


6473 6478 6483 6487 6492 6497 6501 6506 6611 6516 


3 


6620 6625 6530 6534 6539 6544 6548 6553 6568 6562 


4 


6567 6572 6577 6581 6586 6691 6595 6600 6605 6609 


5 


6614 6619 6624 6628 6633 6638 6642 6647 6652 6656 


6 


6661 6666 6670 6676 6680 6685 6689 6694 6699 6703 


7 


6708 6713 6717 6722 6727 6731 6736 6741 6745 6750 


8 


6755 6759 6764 6769 6774 6778 6783 6788 6792 6797 


9 


6802 6806 6811 6816 6820 6825 6830 6834 6839 6844 


930 


96848 96853 96858 96862 96867 96872 96876 96881 96886 96890 


1 


6895 6900 6904 6909 6914 6918 6923 6928 6932 6937 


2 


6942 6946 6961 6956 6960 6965 6970 6974 6979 6984 


3 


6988 6993 6997 7002 7007 7011 7016 7021 7025 7030 


4 


7035 7039 7044 7049 7053 7058 7063 7067 7072 7077 


5 


7081 7086 7090 7095 7100 7104 7109 7114 7118 7123 


6 


7128 7132 7137 7142 7146 7151 7155 7160 7165 7169 


7 


7174 7179 7183 7188 7192 7197 7202 7206 7211 7216 


8 


7220 7225 7230 7234 7239 7243 7248 7263 7267 7262 


9 


7267 7271 7276 7280 7285 7290 7294 7299 7304 7308 


940 


97313 97317 97322 97327 97331 97336 97340 97346 97350 97354 


1 


7359 7364 7368 7373 7377 7382 7387 7391 7396 7400 


2 


7405 7410 7414 7419 7424 7428 7433 7437 7442 7447 


3 


7451 7456 7460 7465 7470 7474 7479 7483 7488 7493 


4 


7497 7502 7506 7511 7516 7520 7525 7629 7634 7639 


5 


7543 7548 7552 7557 7562 7566 7571 7575 7580 7585 


6 


7589 7594 7598 7603 7607 7612 7617 7621 7626 7630 


7 


7635 7640 7644 7649 7653 7658 7663 7667 7672 7676 


8 


7681 7685 7690 7695 7699 7704 7708 7713 7717 7722 


9 


7727 7731 7736 7740 7745 7749 7754 7759 7763 7768 


950 


97772 97777 97782 97786 97791 97795 97800 97804 97809 97813 



508 


TABLE VI.— LOGARITHMS OF NUMBERS. 


N 


0123456789 


950 


97772 97777 97782 97786 97791 97795 97800 97804 97809 97813 


1 


7818 7823 7827 7832 7836 7841 7845 7850 7855 7859 


2 


7864 7868 7873 7877 7882 7886 7891 7896 7900 7905 


3 


7909 7914 7918 7923 7928 7932 7937 7941 7946 7950 


4 


7955 7959 7964 7968 7973 7978 7982 7987 7991 7996 


5 


8000 8005 8009 8014 8019 8023 8028 8032 8037 8041 


6 


8046 8050 8055 8059 8064 8068 8073 8078 8082 8087 


7 


8091 8096 8100 8105 8109 8114 8118 8123 8127 8132 


8 


8137 8141 8146 8150 8155 8159 8164 8168 8173 8177 


9 


8182 8186 8191 8195 8200 8204 8209 8214 8218 8223 


960 


98227 98232 98236 98241 98245 98250 98254 98259 98263 98268 


1 


8272 8277 8281 8286 8290 8295 8299 8^04 8308 8313 


2 


8318 8322 8327 8331 8336 8340 8345 8349 8354 8358 


3 


8363 8367 8372 8376 8381 8385 8390 8394 8399 8403 


4 


8408 8412 8417 8421 8426 8430 8435 8439 8444 8448 


5 


8453 8457 8462 8466 8471 8475 8480 8484 8489 8493 


6 


8498 8502 8507 8511 8516 8520 8525 8529 8534 8538 


7 


8543 8547 8552 8556 8561 8565 8570 8574 8579 8583 


8 


8588 8592 8597 8601 8605 8610 8614 8619 8623 8628 


9 


8632 8637 8641 8646 8650 8655 8659 8664 8668 8673 


970 


98677 98682 98686 98691 98695 98700 98704 98709 98713 98717 


1 


8722 8726 8731 8735 8740 8744 8749 8753 8758 8762 


2 


8767 8771 8776 8780 8784 8789 8793 8798 8802 8807 


3 


8811 8816 8820 8825 8829 8834 8838 8843 8847 8851 


4 


8856 8860 8865 8869 8874 8878 8883 8887 8892 8896 


5 


8900 8905 8909 8914 8918 8923 8927 8932 8936 8941 


6 


8945 8949 8954 8958 8963 8967 8972 8976 8981 8985 


7 


8989 8994 8998 9003 9007 9012 9016 9021 9025 9029 


8 


9034 9038 9043 9047 9052 9056 9061 9065 9069 9074 


9 


9078 9083 9087 9092 9096 9100 9105 9109 9114 9118 


980 


99123 99127 99131 99136 99140 99145 99149 99154 99158 99162 


1 


9167 9171 9176 9180 9185 9189 9193 9198 9202 9207 


2 


9211 9216 9220 9224 9229 9233 9238 9242 9247 9251 


3 


9255 9260 9264 9269 9273 9277 9282 9286 9291 9295 


4 


9300 9304 9308 9313 9317 9322 9326 9330 9335 9339 


5 


9344 9348 9352 9357 9361 9366 9370 9374 9379 9383 


6 


9388 9392 9396 9401 9405 9410 9414 9419 9423 9427 


7 


9432 9436 9441 9445 9449 9454 9458 9463 9467 9471 


8 


9476 9480 9484 9489 9493 9498 9502 9506 9511 9515 


9 


9520 9524 9528 9533 9537 9542 9546 9550 9555 9559 


990 


99564 99568 99572 99577 99581 99585 99590 99594 99599 99603 


1 


9607 9612 9616 9621 9625 9629 9634 9638 9642 9647 


2 


9651 9656 9660 9664 9669 9673 9677 9682 9686 9691 


3 


9695 9699 9704 9708 9712 9717 9721 9726 9730 9734 


4 


9739 9743 9747 9752 9756 9760 9765 9769 9774 9778 


5 


9782 9787 9791 9795 9800 9804 9808 9813 9817 9822 


6 


9826 9830 9835 9839 9843 9848 9852 9856 9861 9865 


7 


9870 9874 9878 9883 9887 9891 9896 9900 9904 9909 


8 


9913 9917 9922 9926 9930 9935 9939 9944 9948 9952 


9 


9957 -9961 9965 9970 9974 9978 9983 9987 9991 9996 


1000 


00000 00004 00009 00013 00017 00022 00026 00030 00035 00039 



INDEX 



Abbott, Dr. Samuel W., 6, 235, 

239, 432. 
Abscissae, 67. 
Accident statistics, 446. 
Accuracy, 26. 

of state censuses, 145. 
Adjusted, and gross death-rates, 
246-249. 

death-rates, 240, 245. 
Adjustment of population, 131. 
Age, census meaning, 166. 

composition, effect on death- 
rate, 231. 

distribution, 165. 

distribution of population, in 
Europe, 182. 

distribution of population in 
United States, 182, 184. 

groups, 170. 

of mother, infant mortality, 363. 

plotting, 73. 

unknown, 171. 
Ages of man, 221. 
American Experience Mortality 
Table, 426. 

Journal of Public Health, 457. 

Public Health Association, 6. 
Analysis of death-rates, 299. 
Appeal to the eye, 60. 
Arithmetical increase, 131, 
Arithmetic probability paper, 395. 
Army diseases, 440, 441. 
Array, 39, 41. 



Averages, 49. 

Average age at death, 374. 
age of persons living, 372. 

Bacterial counts, 26. 
Batt, Dr. W. R., 452. 
Ben Day system, 96. 
BernouiUi's Theorem, 398. 
Bertillon, Louis A., 6. 

Alphonse, 6. 

Jacques, 254. 
Binomial theorem, 381. 
Biometrics, 2. 
Birth-rates, 195. 

Germany and England, 66. 

relation to death-rates, 195. 
Birth registration, 109. 

advantages. 111. 

incomplete. 111. 
Births, standard certificate, 488. 
Blue prints, 96. 

Bolduan, Dr. Charles F., 443, 454. 
Bones, diseases of, 265. 
Boston, adjusted death-rate, 245. 

age distribution of infant 
deaths, 353. 

causes of infant deaths, 356, 359, 
360. 

infant mortality, 348. 

infant mortality by age periods, 
356. 

population density, 152. 

specific death-rates, 235. 



509 



510 



INDEX 



Boston, stillbirths, 340. 

tuberculosis death-rate, 80. 
Bowley, correlation studies, 412. 
Bowleys,rulesf or enumeration, 106. 
Brinton, W. C, 59. 
Brockton, analysis of death-rates, 
303. 

specific death-rates, 305. 
Brooklyn, typhoid fever, 83. 
Burn, Vital Statistics Explained, 
430. 

Cambridge, adjusted death-rate, 
244, 246. 

age distribution of population, 
172, 175, 176. 

causes of death, 65 

deaths distributed by age, 242. 

diphtheria, 320. 

incomplete birth registration, 
112. 

population, 138. 

population density, 152. 

population distributed by age, 
243. 

specific death-rates, 233. 

tuberculosis statistics, 313. 
Cancer, specific death-rates, 335. 

statistics, 334. 
Causal relations, 402. 
Causality and correlation, 404. 
Causation, laws of, 405. 

and correlation, 420. 
Causes of death, 254. 

infants, 356,. 359, 360. 

international list, 257. 
Census date, 100. 

U. S., 100. 
Certificate of birth, standard, 489. 

of death, standard, 490. 
Chad wick, Edwin, 6. 



Chance, 379. 
element in sanitation, 394. 
natural phenomena, 382. 
Chapin, Dr. Charles V., 323, 324, 

451. 
Charts, 93. 
Chicago, Municipal Tuberculosis 

Sanitorium, 413. 
Child mortality, 346. 
Childhood, early, diseases, 369. 
mortality, 368. 
proportionate mortality, 370. 
Children's Bureau, U. S. Dep't of 

Labor, 361, 365. 
Children, specific death-rates, 369. 
Chronological changes in death- 
rates, 234. 
changes in vital rates, 210. 
Cincinnati, population estimates, 

140. 
Circulatory system, diseases of, 

261. 
Cities, rate of growth, 137. 
Civil divisions, 103. 
Classes, 39, 40. 
Classification, 39. 

of diseases in 1850, 256. 
of population, 161. 
Coefficient of variation, 388, 389. 
Coin tossing, 379, 381. 
Collection of data, 17. 
Color in diagrams, 93. 
Component part diagrams, 95. 
Concealed classification, 238. 
Conception of frequency curve, 

399. 
Connecticut, measles and grippe, 

410. 
Consumption (see Tuberculosis). 
Corrected death-rates, 189, 239. 
Correlation, 402. 



INDEX 



511 



Correlation, and causality, 404. 

color of water and typhoid fever, 
411. 

example, 410. 

Galton's coefficient, 409. 

housing and tuberculosis, 413. 

methods, 407. 

mosquitoes and malaria, 419. 

secondary, 415. 

shown graphically, 411. 

spurious, 416. 

table, 413, 415. 

use by epidemiologists, 418. 

vaccination and influenza, 420. 

water filtration and typhoid 
fever, 416. 
Credibility of census, 106. 
Cross-section paper, 87, 90. 
Cumulative grouping, 48. 

plotting, 75. 
Curves, equation of, 98. 

Davis, Dr. W. H., 358. 
Death, average age, 374. 

certificate, standard, 276, 490. 

registration, uses of, 115. 
Deaths, registration of, 113. 
Death-rates, 186. 

adjusted to standard popula- 
tion, 240. 

analysis of, 299. 

effect of size of place, 192. 

limited use, 216. 

precision, 187. 

relations to birth-rates, 195. 
Deceptions, graphical, 61. 
Demographers, 5. 
Demography, science, 1. 

divisions, 2. 

influence of war, 442. 
Density of population, 150. 



Detroit, population of, 138. 
Deviation from mean, 385. 

standard, 387. 
Diagrams, types of, 59, 63. 
Digestive system, 262. 
Diphtheria, age susceptibility, 323. 

fatality, 324. 

in Cambridge, 320. 

in Massachusetts, 325. 

in Providence, 323, 324. 

urban and rural, 325. 
Divorce-rates, 200, 216. 
Double coordinates, 81. 
Doubtful observations, 391. 
Dry statistics, 8. 
Dublin, Dr. Louis I., Ill, 369. 
Dwellings, number of persons in, 
164. 

Earnings of father, infant mor- 
tality, 365, 366. 

Economic conditions and health, 
445. 

Education, infant mortality, 363. 

Elderton, correlation, 411. 

Endemic index, 454. 
median, 454. 

Enforcement of registration law^ 
111. 

England, vital statistics of, 12, 
210. 

Enumeration, 17, 100. 

Equation of curves, 98, 415. 

Error of statistics, 19. 

Error, probable, 390. 

Errors in age, 167. 

in published death-rates, 192 
in round numbers, 168. 

Estimates of population, 129, 137, 
139. 

Eugenics, 2. 



512 



INDEX 



Expectation of life, 428, 434. 

formulas for, 430. 

infants, 355. 
External causes of death, 266. 

Fallacy of concealed classification, 

238. 
Families, number of persons in, 

164. 
Farr, Dr. William, 6, 254, 255. 
Fatality rate, 309. 

of diphtheria, 324. 

of typhoid fever, 330. 
Fecundity, 196. 

relation to age, 198. 
Feeding, infant mortality, 364. 
Final death-rate, 191. 
First-year death-rate, 343. 
Fisher, Arne, 430. 
France, vital statistics of, 12, 210. 
Frequency curve, 378. 

curve as a conception, 399. 

natural, 376. 
Frankel, Dr. Lee K., 122. 

Galton, Sir Francis, 3, 5, 6. 
Galton's coefficient of correlation, 

409. 
Garment workers, health of, 446. 
Genealogy, 2. 
General death-rates, 186. 

diseases, 257. 

vital rates, use of, 204. 
Generalization, 39, 40. 
Genito-urinary system, diseases 

of, 262. 
Geometric mean, 50. 
Geometrical increase, 132, 133. 
Germany, vital rates, 210. 
Glover, Prof. James W., 433. 
Gonorrhoea reportable, 120. 



Graphical deceptions, 61. 

method of estimating popula- 
tion, 141. 

Graphics, statistical, 58. 

Graunt, Capt. John, 3, 4, 6. 

Great war, effect on demography, 
442. 

Gross death-rates, 186. 

Group designations, 45. 

Group plotting, 71, 74. 

Grouping, cumulative, 48. 
percentage, 47. 

Groups, 39, 40, 43. 

Guilfoy, Dr., 432. 

Gummed letters, 94. 

Halley, Edmund, 4. 

Hamburg, infant mortality, 341, 
343, 344, 353. 

Harmonic mean, 52. 

Hazen's theorem, 450. . 

Health officer, use of statistics, 
11. 

Heights of soldiers, 377, 383, 395. 

Higher ages, proportionate mor- 
tality, 372. 

Hoffman, Dr. F. L., 334, 338. 

Hollerith punching machine, 54. 

Holt, Dr. Wm. L., 245. 

Homes and infant mortality, 361. 

Horizontal scale, 69, 

Hospital discharge certificate, 471.* 

Hospital statistics, 443. 

Housing and tuberculosis, 413. 

Household duties, infant mortal- 
ity, 364. 

Hungary, vital rates, 210. 

Ideal death-rate, 216. 
Ill-defined diseases, 267. 
Illegitimate births, 198. 



INDEX 



513 



Immigration, 141, 142. 
Incompleteness of morbidity sta- 
tistics, 119. 
Increase, natural rate of, 203. 
Index, 31. 

of concentration, round num- 
bers, 169. 
Induction, 14. 
Industrial accidents, 446. 

classification, 280. 

statistics, 443. 
Inexact numbers, 24, 26. 
Infancy, diseases of, 265. 
Infant deaths, age distribution in 
Boston, 353. 

causes, Johnstown, 360. 
Infant mortality, 339. 

age of mother, 363. 

age periods, 355. 

and homes, 361. 

birth attendance, 362. 

Boston, 348. 

education, 363. 

father's earnings, 365, 366. 

feeding, 364. 

foreign cities, 350. 

household duties, 364. 

methods of statement, 345. 

order of birth, 366. 

problems, 367. 

reasons for decrease, 349. 

sleeping rooms, 362. 

Sweden, 345. 

U. S. cities, 351. 

ventilation, 362. 
Infants, causes of death, Boston, 
356. 

deaths at different ages, 352. 
Infants, definitions, 339. 

expectation of life, 355. 

life tables, 354. 



Infants, proportionate mortality, 
344. 
specific death-rates, 341. 
International classification of dis- 
eases, 254. 
list of causes of death, 255, 257. 
Irregular group plotting, 72. 

Jarvis, Edward, 6, 108. 
Jevons, W. Stanley, 10, 403. 
Johnson, George A., 332. 
Johnstown, first year mortality, 
344. 

stillbirths, 341. 

studies, 360, 361. 
Joint causes of death, 276. 

Kensington, birth-rates, 199. 
King, 404. 

Lag, 417, 418. 

Laplace, probability studies, 4. 
Lathrop, Miss Julia C, 361. 
Lead-poisoning, 444. 
Least squares, 386. 
Lettering, 91, 92. 
Life-rates, 424. 
Life tables, 422. 

based on living populations, 
430. 

early history, 431. 

infants, 354. 

recent, 431. 
Living persons, average age, 372. 

median age, 373. 
Local death-rates, 190. 
Logarithmic paper, 87. 

plotting, 85, 88. 
Logarithms, 34, 84. 

table of, 491. 
Logic, use of, 9. 



614 



INDEX 



Lowell, analysis of death-rates, 
303. 
specific death-rates, 305. 

Malformations, 265. 
Malthus, 4. 
Maps, statistical, 96. 
Marital condition, effect on death- 
rates, 229. 
Marriage-rates, 200, 215. 
Marriage registration, 115. 
Massachusetts, age distribution, 
169. 

analysis of death-rates, 300. 

birth-rates, 212. 

causes of deaths, 310. 

causes of divorce, 201. 

death-rates, 1900-10, 212. 

death-rates by counties, 302. 

death-rates of cities, 303. 

death-rates plotted, 396. 

diphtheria, 325. 

divorce-rates, 201, 216. 

errors in death-rates, 194. 

General Hospital, 444. 

infant mortahty, 347. 

marriage-rates, 215. 

monthly death-rates, 214. 

morbidity registration, 116. 

population estimates, 140. 

seasonal mortality, 306. 

specific death-rates, 236. 

tuberculosis deaths by years, 
317. 

tuberculosis death-rate, 79. 

variations in death-rates, 397. 

venereal diseases, 120. 
Maternal mortality, 367. 
Mechanical computers, 53. 
Mechanics of diagrams, 89. 
Median, 42. 



Median age of living persons, 373. 
Medical examiners, 278. 
Metropolitan districts, 161. 
Military statistics, 437. 
Mill, John Stuart, 406. 
Mills-Reincke, phenomenon, 450. 
Mirza, vision of, 224. 
Misuse of rates, 30, 
Model state law, births and 
deaths, 472. 

state law, morbidity, 465. 
Monographic method, 14. 
Monthly death-rates, 214. 
Morbidity registration, 116. 

model law, 117. 

rate, 309. 

reports, model law, 465. 

standard blank, 470. 
Mortahty rate, 308, 425. 
Moscow, death-rates, 78. 
Most probable life-time, 427. 
Moving average, 53. 

National Health Department, 128. 

statistics, 127. 

vital statistics, 12. 
Nationahty, effect on death-rate, 

230. 
Natural frequency, 376. 
Nervous system, diseases of, 260. 
New Jersey, tuberculosis, 318. 
New South Wales, 226, 241. 
N'ew York City, maternal mortal- 
ity, 367. 

life tables, 432. 

resident death-rates, 191. 
New York, tuberculosis, 320. 
Newsholme, 199. 
Nightingale, Florence, 5, 6. 
Non-reportable diseases, 120. 
Normalized average, 454. 



INDEX 



515 



Nosography, 254. 
Nosology, 254. 

not exact science, 297. 
Notifiable diseases, 118. 
Notification, 107. 

Occupation and tuberculosis, 318. 
Occupation, index, 280. 
Occupations, list of, 281. 
Old age, diseases of, 265. 
One scale diagrams, 64. 
Optical illusions, 62. 
Ordinates, 67. 

Panics, relation to birth-rates, 

213. 
Particular diseases, adjustments 

of death-rates, 251. 
Pathometrics, 2. 
Pearson, Karl, 3, 5, 224, 385. 
Percentage grouping, 47. 

of mortality, 308. 
Peddle 's Graphical Charts, 98. 
Physical examinations, 123. 
Physicians' pocket reference, 256. 
Plotting, 66, 70. 

paper, 90. 
Poates Engraving Company, 98. 
Polar coordinates, 81. 
Poliomyelitis, age distribution, 48, 

448. 
Population, 129. 

age distribution, Europe, 182. 

estimates, 211. 

race, color, nativity, etc., 161. 

rate of increase, 136. 

redistributed by age, 172. 

types, 178. 
Powers' statistical machines, 54. 
Precision, 26. 
Precision of death-rates, 187. 



Preliminary death-rate, 191. 
Prenatal deaths, 340. 
Primary cause of death, 278. 
Probability of living a year, 422. 
Probability paper, 393, 398. 
Probability, use of, 398. 
Probability scale, 391. 
Probable error, 390. 
Progressive, character of age dis- 
tribution, 175. 

type of population, 178. 
Proportionate mortality, 308. 

childhood, 370. 

higher ages, 372. 

U. S., 95. 
Providence, diphtheria, 323, 324. 
Puerperal state, diseases of, 263, 

Quartiles, 42. 

Quetelet, probability studies, 5. 

Race and tuberculosis, 319. 

effect on death-rate, 234. 
Racial adjustments of death-rates, 
249. 

composition of population, 162. 
Radial plotting, 82. 
Rainfall plotting, 68. 
Rates, 29, 32. 
Ratios, 27. 

Ratio cross-section paper, 83. 
Rectangular coordinates, 66. 
Redistribution of population, 172, 

174. 
References, 459. 

Regressive type of population, 178. 
Registrars, laxity of, 112. 
Registration, 17, 100, 107, 113. 

area for deaths, 123. 

area for births, 127. 

of morbidity, 116. 



516 



INDEX 



Registration of marriages, 115. 
Registration, model law, 472, 
Reinhardt's lettering, 91. 
Reports, publication of, 455. 
Reports, standards, 457. 
Representative method, 14. 
Reproduction of diagrams, 97. 
Resident, death-rates, 190. 
Respiratory system, 261. 
Restricted death-rates, 220. 
Revised death-rates, 192. 

estimates of population, 138. 
Richmond, tuberculosis, 320. 
Rochester, population estimates, 

140. 
Round numbers, error of, 168. 
Rural and urban population, 146, 

149. 

Sanitary index, 451. 

Saxelby's mathematics, 98. 

Scales, choice of, 77. 

Schedules of enumeration, 103. 

School age, mortality of children, 
371. 

Seasonal, deaths from tuberculo- 
sis, 315. 
distribution of typhoid fever, 

331, 332. 
mortality, 306. 

Secondary correlation, 415, 418. 

Sedgwick and MacNutt, 450. 

Senility, 265. 

Series, 39. 

Set-backs, 417. 

Sex distribution, 163. 

Shattuck, Lemuel, 108. 

Short term death-rates, 194. 

Sickness, surveys, 122. 

Skew curves, 383. 

Skin, diseases of, 264. 



Sleeping rooms and infant mor- 
tality, 362. 
Slide rule, 35. 
Smith, Adam, 4. 
Soldiers, heights of, 377, 383, 

395. 
Specific death-rates, 220, 225, 
252. 

by age and sex, 227. 

use of, 239. 

U. S., 435. 
Specific life-rates, 424. 
Springfield, population estimate, 

143. 
Spurious correlation, 416. 
Standard, birth certificate, 109. 

certificates, 488, 490. 

certificate of death, 113, 276. 
Standardized death-rates, 239. 

Standard, deviation, 387. 

morbidity blank, 470. 

million, 181. 
State censuses, 145. 
States in registration area, 125. 
State sanitation, 108. 
Stationary type of population, 

178. 
Statistical, graphics, 58. 

induction, 14. 

maps, 96. 

method, 6, 14. 

processes, 17. 

units, 18. 
Statistics, history of, 3. 
Stillbirths, 195, 340. 
Summation diagrams, 75, 385. 
Sundbarg, 12, 178. 
Stissmilch, Peter, 4. 
Sweden, age distribution, 180. 

increase in population, 203. 

infant mortality, 345. 



INDEX 



517 



Sweden, progressive age distribu- 
tion, 177. 

vital statistics of, 12. 

vital rates, 204. 
Syphilis reportable, 120. 

Tabulation, 20. 
Tally sheets, 20. 
Time plotting, 69. 
Tuberculosis, age and sex, 311. 

and housing, 413. 

and occupation, 318. 

and race, 319. 

Boston, 80. 

death-rate, 79. 

proportionate mortality, 316. 

N. Y. and Richmond, 320. 

seasonal distribution of deaths, 
315. 
Typhoid fever, age distribution, 
47, 328. 

and water filtration, 333. 

Brooklyn, 83. 

case fatality, 330. 

chronological changes, 332. 

seasonal changes, 331, 332. 

specific death-rates by ages, 329. 

statistical study, 327. 

synonyms, 275. 

Undesirable terms for causes of 

death, 271. 
Undertaker, certificate, 114. 
United States army, vital statis- 
tics, 438, 439. 
cancer statistics, 335. 
causes of death, 311. 
census, 100. 
cities, increase in number, 149. 



United States, cities, list of popu- 
lations, 154. 

life tables, 429, 433, 434. 

population plotted, 88. 

proportionate mortality, 95. 

registration area of births, 127. 

registration area for deaths, 123. 

tuberculosis statistics, 315. 

vital statistics of, 12. 
Units, statistical, 18. 
Urban and rural population, 146, 
149. 

Variation, coefficient, 388, 389. 
Variations in death-rate, 192. 
Venereal diseases, reportable, 120. 
Ventilation, infant mortality, 362. 
Vie probable, 427. 
Vision of Mirza, 224. 
Vital, bookkeeping, 10. 

rates, chronological changes, 
210. 

statistics, current use, 452. 

Wall charts, 93. 

War, effect on demography, 442. 

Water filtration and typhoid fever, 

333. 
Wax process, 98. 
Wedding-rates, 200. 
Weighted average, 50. 
Westergaard, 7, 404. 
Whipple, George C, 108. 
Whitechapel, birth-rates, 199. 
Willcox, Walter F., 229, 334. 
Wright, Carroll D., 6. 

Zinc process, 97. 




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